\n* Higher Auslander-Reiten theory in the sense of Iyama

\n* Wald hausen K-theory of differential graded categories\n\nIf time permits\, as a first application of the above relationship\, I\nwill outline a symplect o-geometric proof of a recent result of Beckert\nconcerning the derived eq uivalence between higher Auslander algebras of\ndifferent dimensions. This is a report on joint work with Tobias\nDyckerhoff and Yankı Lekili.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Baptiste Rognerud (University of Paris) DTSTART;VALUE=DATE-TIME:20200608T120000Z DTEND;VALUE=DATE-TIME:20200608T123000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/8 DESCRIPTION:Title: Combinatorics of quasi-hereditary structures\, I\ nby Baptiste Rognerud (University of Paris) as part of Paris algebra semin ar\n\n\nAbstract\nQuasi-hereditary algebras were introduced by Cline\, Par shall and Scott as a tool to study highest weight theories which arise in the representation theories of semi-simple complex Lie algebras and reduct ive groups. Surprisingly\, there are now many examples of such algebras\, such as Schur algebras\, algebras of global dimension at most two\, incide nce algebras and many more.\n\nA quasi-hereditary algebra is an Artin alge bra together with a partial order on its set of isomorphism classes of sim ple modules which satisfies certain conditions. In the early examples the partial order predated (and motivated) the theory\, so the choice was clea r. However\, there are instances of quasi-hereditary algebras where there is no natural choice for the partial ordering and even if there is such a natural choice\, one may wonder about all the possible orderings.\nIn this talk we will explain that all these choices for an algebra $A$ can be org anized in a finite partial order which is in relation with the tilting the ory of $A$. In a second part of the talk we will focus on the case where $ A$ is the path algebra of a Dynkin quiver.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuta Kimura (Bielefeld) DTSTART;VALUE=DATE-TIME:20200608T123000Z DTEND;VALUE=DATE-TIME:20200608T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/9 DESCRIPTION:Title: Combinatorics of quasi-hereditary structures\, II \nby Yuta Kimura (Bielefeld) as part of Paris algebra seminar\n\n\nAbstrac t\nQuasi-hereditary algebras were introduced by Cline\, Parshall and Scott as a tool to study highest weight theories which arise in the representat ion theories of semi-simple complex Lie algebras and reductive groups. Sur prisingly\, there are now many examples of such algebras\, such as Schur a lgebras\, algebras of global dimension at most two\, incidence algebras an d many more.\n\nA quasi-hereditary algebra is an Artin algebra together wi th a partial order on its set of isomorphism classes of simple modules whi ch satisfies certain conditions. In the early examples the partial order p redated (and motivated) the theory\, so the choice was clear. However\, th ere are instances of quasi-hereditary algebras where there is no natural c hoice for the partial ordering and even if there is such a natural choice\ , one may wonder about all the possible orderings.\nIn this talk we will e xplain that all these choices for an algebra $A$ can be organized in a fin ite partial order which is in relation with the tilting theory of $A$. In a second part of the talk we will focus on the case where $A$ is the path algebra of a Dynkin quiver.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Christof Geiss (UNAM) DTSTART;VALUE=DATE-TIME:20200615T120000Z DTEND;VALUE=DATE-TIME:20200615T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/10 DESCRIPTION:Title: Generic bases for surface cluster algebras\nby C hristof Geiss (UNAM) as part of Paris algebra seminar\n\n\nAbstract\nThis is a report on joint work with D. Labardini-Fragoso and J. Schröer. We sh ow that for most marked surfaces with non-empty boundary\, possibly with p unctures\, the generic Caldero-Chapoton functions form a basis of the corr esponding cluster algebras for any choice of geometric coefficients. For s urfaces without punctures the $\\tau$-reduced components of the correspond ing gentle Jacobian algebra are naturally parametrized by X-laminations of the surface\, and it is easy to see that for principal coefficients\, the generic basis coincides with the bangle basis introduced by Musiker-Schif fler-Williams.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 / END:VEVENT BEGIN:VEVENT SUMMARY:Myungho Kim (Kyung Hee University\, Seoul) DTSTART;VALUE=DATE-TIME:20200622T120000Z DTEND;VALUE=DATE-TIME:20200622T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/11 DESCRIPTION:Title: Braid group action on the module category of quantum affine algebras\nby Myungho Kim (Kyung Hee University\, Seoul) as par t of Paris algebra seminar\n\n\nAbstract\nLet $g_0$ be a simple Lie algebr a of type $ADE$ and let $U′_q(g)$ be the corresponding untwisted quantum affine algebra. We found an action of the braid group $B(g_0)$ on the qua ntum Grothendieck ring $K_t(g)$ of Hernandez-Leclerc's category $C^0_g$. I n the case of $g_0=A_{N−1}$\, we construct a monoidal autofunctor $S_i$ for each integer $i$ on a category $T_N$ arising from the quiver Hecke al gebra of type $A_\\infty$. \nSince there is an isomorphism between the Gro thendieck ring $K(T_N)$ of $T_N$ and the quantum Grothendieck ring $K_t(A^ (1)_{N−1})$\, the functors $S_i$\, $(i=1\, ...\, N-1)$\, recover the act ion of the braid group $B(A_{N−1})$. \nThis is a joint work with Masaki Kashiwara\, Euiyong Park and Se-jin Oh.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 / END:VEVENT BEGIN:VEVENT SUMMARY:Osamu Iyama (Nagoya) DTSTART;VALUE=DATE-TIME:20200713T120000Z DTEND;VALUE=DATE-TIME:20200713T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/13 DESCRIPTION:Title: Tilting theory of contracted preprojective algebras and cDV singularities\nby Osamu Iyama (Nagoya) as part of Paris algebr a seminar\n\n\nAbstract\nA preprojective algebra of non-Dynkin type has a family of tilting modules associated with the elements in the correspondin g Coxeter group W. This family is useful to study the representation theor y of the preprojective algebra and also to categorify cluster algebras.\nI n this talk\, I will discuss tilting theory of a contracted preprojective algebra\, which is a subalgebra eAe of a preprojective algebra A given by an idempotent e of A. It has a family of tilting modules associated with t he chambers in the contracted Tits cone. They correspond bijectively with certain double cosets in W modulo parabolic subgroups. \nI will apply thes e results to classify a certain family of reflexive modules over a cDV sin gularities R\, called maximal modifying (=MM) modules. We construct an inj ective map from MM R-modules to tilting modules over a contracted preproje ctive algebra of extended Dynkin type. This is bijective if R has at worst an isolated singularity. We can recover previous results (Burban-I-Keller -Reiten\, I-Wemyss) as a very special case.\nThis is joint work with Micha el Wemyss.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 / END:VEVENT BEGIN:VEVENT SUMMARY:Linyuan Liu (刘琳媛) (Sydney) DTSTART;VALUE=DATE-TIME:20200629T120000Z DTEND;VALUE=DATE-TIME:20200629T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/14 DESCRIPTION:Title: Modular Brylinski-Kostant filtration of tilting modu les\nby Linyuan Liu (刘琳媛) (Sydney) as part of Paris algebra semi nar\n\n\nAbstract\nLet $G$ be a reductive algebraic group over a field $k$ . When $k=\\mathbb{C}$\, R. K. Brylinski constructed a filtration of weigh t spaces of a $G$-module\, using the action of a principal nilpotent eleme nt of the Lie algebra\, and proved that this filtration corresponds to Lus ztig's $q$-analogue of the weight multiplicity. Later\, Ginzburg discovere d that this filtration has an interesting geometric interpretation via the geometric Satake correspondence. Recently\, we managed to generalise this result to the case where $k$ is a field of good positive characteristics. I will give a brief introduction to both historical results and our new r esult in the talk.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 / END:VEVENT BEGIN:VEVENT SUMMARY:Xin Fang (房欣) (Cologne) DTSTART;VALUE=DATE-TIME:20200706T120000Z DTEND;VALUE=DATE-TIME:20200706T123000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/15 DESCRIPTION:Title: Exact structures and degenerations of Hall algebras\ , I\nby Xin Fang (房欣) (Cologne) as part of Paris algebra seminar\n \n\nAbstract\nIn this talk\, we will explain relations between exact struc tures on an additively finite additive category and degenerations of the a ssociated Hall algebras. The first part of the talk will be devoted to the main motivation provided by concrete examples of degenerations of negativ e parts of quantum groups arising as Hall algebras of quiver representatio ns. We will then turn to Lie theory in order to establish a link from thes e examples to tropical flag varieties and certain quiver Grassmannians. In the second part of the talk we will present results in the general case a nd sketch their proofs based on Auslander-Reiten theory. If time permits\, we will briefly discuss further conjectural examples and generalizations. \n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 / END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Gorsky (Stuttgart) DTSTART;VALUE=DATE-TIME:20200706T123000Z DTEND;VALUE=DATE-TIME:20200706T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/16 DESCRIPTION:Title: Exact structures and degenerations of Hall algebras\ , II\nby Mikhail Gorsky (Stuttgart) as part of Paris algebra seminar\n \n\nAbstract\nIn this talk\, we will explain relations between exact struc tures on an additively finite additive category and degenerations of the a ssociated Hall algebras. The first part of the talk will be devoted to the main motivation provided by concrete examples of degenerations of negativ e parts of quantum groups arising as Hall algebras of quiver representatio ns. We will then turn to Lie theory in order to establish a link from thes e examples to tropical flag varieties and certain quiver Grassmannians. In the second part of the talk we will present results in the general case a nd sketch their proofs based on Auslander-Reiten theory. If time permits\, we will briefly discuss further conjectural examples and generalizations. \n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 / END:VEVENT BEGIN:VEVENT SUMMARY:Liran Shaul (Prague) DTSTART;VALUE=DATE-TIME:20200914T120000Z DTEND;VALUE=DATE-TIME:20200914T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/17 DESCRIPTION:Title: The Cohen–Macaulay property in derived algebraic g eometry\nby Liran Shaul (Prague) as part of Paris algebra seminar\n\n\ nAbstract\nIn this talk\, we explain how to extend the theory of Cohen-Mac aulay\nrings to the setting of commutative non-positive DG-rings. By study ing\nlocal cohomology in the DG-setting\, one obtains certain amplitude\ni nequalities about certain DG-modules of finite injective dimension.\nWhen these inequalities are equalities\, we arrive at the notion of a\nCohen-Ma caulay DG-ring.\n\nWe then show that these arise naturally in many situati ons\, and\nexplain their basic theory. We explain that any derived quotien t of a \nCohen-Macaulay ring is Cohen-Macaulay\,\nand show that Cohen-Maca ulayness is the generic local situation in\nderived algebraic geometry: un der mild hypothesis\, every eventually\ncoconnective locally noetherian de rived scheme is Cohen-Macaulay on a\ndense open set.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/17 / END:VEVENT BEGIN:VEVENT SUMMARY:Zhengfang Wang (Stuttgart) DTSTART;VALUE=DATE-TIME:20200928T120000Z DTEND;VALUE=DATE-TIME:20200928T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/18 DESCRIPTION:Title: $B_\\infty$-algebras and Keller’s conjecture for s ingular Hochschild cohomology\nby Zhengfang Wang (Stuttgart) as part o f Paris algebra seminar\n\n\nAbstract\nWe first give a basic introduction to $B_\\infty$-algebras. Then from a $B_\\infty$-algebra A\, we contruct two new $B_\\infty$-algebras by using two different swapping maps: the opp osite $B_\\infty$-algebra and the transpose $B_\\infty$-algebra. Quite sur prisingly\, we show that under a certain condition on A (satisfied\, for i nstance\, by brace $B_\\infty$-algebras or Gerstenhaber-Voronov algebras) these two $B_\\infty$-algebras are naturally isomorphic\, which is motivat ed from Kontsevich-Soibelman's minimal operad. \n\nWe also explain the rol e of the above result in the proof of Keller's conjecture for singular Hoc hschild cohomology in the case of radical square zero algebras. This is jo int work with Xiaowu Chen and Huanhuan Li.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/18 / END:VEVENT BEGIN:VEVENT SUMMARY:Maria Julia Redondo (Bahia Blanca) DTSTART;VALUE=DATE-TIME:20200921T120000Z DTEND;VALUE=DATE-TIME:20200921T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/19 DESCRIPTION:Title: $L_\\infty$-structure on Barzdell's complex for mono mial algebras\nby Maria Julia Redondo (Bahia Blanca) as part of Paris algebra seminar\n\n\nAbstract\nWhen dealing with a monomial algebra $A$\, Bardzell’s complex $B(A)$ has shown to be more efficient for computing H ochschild cohomology groups of $A$ than the Hochschild complex $C(A)$.\nSi nce $C(A)[1]$ is a dg Lie algebra\, it is natural to ask if the comparison morphisms between these complexes allows us to transfer the dg Lie struct ure to $B(A)[1]$. This is true for radical square zero algebras\, but it is not true in general for monomial algebras.\nIn this talk\, I will descr ibe an explicit $L_\\infty$-structure on $B(A)$ that induces a weak equiva lence of $L_\\infty$-algebras between $B(A)$ and $C(A)$. This allows us t o describe the Maurer-Cartan equation in terms of elements of degree 2 in $B(A)$ and make concrete computations when $A$ is a truncated monomial alg ebra.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/19 / END:VEVENT BEGIN:VEVENT SUMMARY:Dylan Allegretti (UBC Vancouver) DTSTART;VALUE=DATE-TIME:20201005T120000Z DTEND;VALUE=DATE-TIME:20201005T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/20 DESCRIPTION:Title: Wall-crossing and differential equations\nby Dyl an Allegretti (UBC Vancouver) as part of Paris algebra seminar\n\n\nAbstra ct\nThe Kontsevich-Soibelman wall-crossing formula describes the wall-cros sing behavior of BPS invariants in Donaldson-Thomas theory. It can be form ulated as an identity between (possibly infinite) products of automorphism s of a formal power series ring. In this talk\, I will explain how these s ame products also appear in the exact WKB analysis of Schrödinger's equat ion. In this context\, they describe the Stokes phenomenon for objects kno wn as Voros symbols.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/20 / END:VEVENT BEGIN:VEVENT SUMMARY:Ryo Fujita (Paris\, IMJ-PRG) DTSTART;VALUE=DATE-TIME:20201012T120000Z DTEND;VALUE=DATE-TIME:20201012T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/22 DESCRIPTION:Title: Twisted Auslander-Reiten quivers\, quantum Cartan ma trix and representation theory of quantum affine algebras\nby Ryo Fuji ta (Paris\, IMJ-PRG) as part of Paris algebra seminar\n\n\nAbstract\nFor a complex simple Lie algebra $g$\, its quantum Cartan matrix plays an impor tant role in the representation theory of the quantum affine algebra of $g $. When $g$ is of type ADE\, Hernandez-Leclerc (2015) related its quantum Cartan matrix with the representation theory of Dynkin quivers and hence w ith the combinatorics of adapted words in the Weyl group of the correspond ing ADE type. In this talk\, we introduce the notion of Q-data\, which can be regarded as a combinatorial generalization of a Dynkin quiver with hei ght function\, and its twisted Auslander-Reiten quiver. Using them\, we re late the quantum Cartan matrix of type BCFG with the combinatorics of twis ted adapted words in the Weyl group of the corresponding unfolded ADE type introduced by Oh-Suh (2019). Also\, we see their relation to the represen tation theory of quantum affine algebras. For example\, we present a (part ially conjectural) unified expression of the denominators of R-matrices be tween the Kirillov-Reshetikhin modules in terms of the quantum Cartan matr ices. This is a joint work with Se-jin Oh.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/22 / END:VEVENT BEGIN:VEVENT SUMMARY:Norihiro Hanihara (Nagoya) DTSTART;VALUE=DATE-TIME:20201019T120000Z DTEND;VALUE=DATE-TIME:20201019T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/23 DESCRIPTION:Title: Cluster categories of formal dg algebras\nby Nor ihiro Hanihara (Nagoya) as part of Paris algebra seminar\n\n\nAbstract\nCl uster categories are Calabi-Yau triangulated categories endowed with clust er tilting objects. They have played an important role in the (additive) c ategorification of cluster algebras. We study the version developed by Ami ot-Guo-Keller\, which is defined in terms of CY dg algebras. Given a negat ively graded (non-dg) CY algebra\, we view it as a dg algebra with trivial differential. We give a description of the cluster category of such a for mal dg algebra as the triangulated hull of an orbit category of a derived category\, and also as the singularity category of a finite dimensional al gebra. Furthermore\, if time permits\, we will talk about a certain conver se of this construction\, giving a \nMorita-type theorem for CY triangulat ed categories arising from hereditary algebras\, partially generalizing th at of Keller-Reiten.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/23 / END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane Launois (Kent) DTSTART;VALUE=DATE-TIME:20201109T130000Z DTEND;VALUE=DATE-TIME:20201109T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/24 DESCRIPTION:Title: Catenarity and Tauvel’s height formula for quantum nilpotent algebras\nby Stéphane Launois (Kent) as part of Paris alge bra seminar\n\n\nAbstract\nThis talk is based on joint work with Ken Goode arl and Tom Lenagan. \nI will explain why quantum nilpotent algebras are catenary\, that is\, why all saturated chains of inclusions of prime ideal s in a quantum nilpotent algebra have the same length. As a corollary\, we obtain that Tauvel’s height formula holds for quantum nilpotent algebra s. Time permitting\, \nI will present a different strategy to prove the la tter result.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/24 / END:VEVENT BEGIN:VEVENT SUMMARY:Wai-kit Yeung (Tokyo\, IPMU) DTSTART;VALUE=DATE-TIME:20201026T130000Z DTEND;VALUE=DATE-TIME:20201026T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/25 DESCRIPTION:Title: Pre-Calabi-Yau algebras\nby Wai-kit Yeung (Tokyo \, IPMU) as part of Paris algebra seminar\n\n\nAbstract\nPre-Calabi-Yau ca tegories are algebraic structures first studied by Kontsevich and Vlassopo ulos. They can be viewed as a noncommutative analogue of Poisson structure s\, just like Calabi-Yau structures can be viewed as a noncommutative anal ogue of symplectic structures. In this talk\, we discuss several aspects o f this notion.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/25 / END:VEVENT BEGIN:VEVENT SUMMARY:Eleonore Faber (Leeds) DTSTART;VALUE=DATE-TIME:20201116T130000Z DTEND;VALUE=DATE-TIME:20201116T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/26 DESCRIPTION:Title: McKay quivers of complex reflection groups and the M cKay correspondence\nby Eleonore Faber (Leeds) as part of Paris algebr a seminar\n\n\nAbstract\nFinite complex reflection groups were classified by Shepherd\nand Todd: up to finitely many exceptions they are the groups G(r\,p\,n).\nIn this talk we give a combinatorial description of the McKay quivers of\nthese groups. Further we will comment on a McKay corresponden ce for\ncomplex reflection groups. This is joint work with R.-O. Buchweitz \, C.\nIngalls\, and M. Lewis.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/26 / END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Scherotzke (Luxembourg) DTSTART;VALUE=DATE-TIME:20201123T130000Z DTEND;VALUE=DATE-TIME:20201123T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/27 DESCRIPTION:Title: Cotangent complexes of moduli spaces and Ginzburg dg algebras\nby Sarah Scherotzke (Luxembourg) as part of Paris algebra s eminar\n\n\nAbstract\nWe start by giving an introduction to the notion of moduli stack of a dg category. Then we will explain what shifted symplecti c structures are and how they are connected to Calabi-Yau structures on dg categories. More concretely\, we will show that the cotangent complex of the moduli stack of a dg category A is isomorphic to the moduli stack of t he *Calabi-Yau completion* of A. This answers a conjecture of Keller-Yeung . This is joint work with Damien Calaque and Tristan Bozec available on the arXiv.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/27 / END:VEVENT BEGIN:VEVENT SUMMARY:Elie Casbi (MPI Bonn) DTSTART;VALUE=DATE-TIME:20201102T130000Z DTEND;VALUE=DATE-TIME:20201102T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/28 DESCRIPTION:Title: Equivariant multiplicities of simply-laced type flag minors\nby Elie Casbi (MPI Bonn) as part of Paris algebra seminar\n\n \nAbstract\nThe study of remarkable bases of (quantum) coordinate rings ha s been an area of\nintensive research since the early 90's. For instance\, the multiplicative properties of \nthese bases (in particular the dual ca nonical basis) was one of the main motivations for\nthe introduction of cl uster algebras by Fomin and Zelevinsky around 2000. \nIn recent work\, Bau mann-Kamnitzer-Knutson introduced an algebra morphism \n$\\overline{D}$ f rom the coordinate algebra $\\mathbb{C}[N]$ of a maximal unipotent subgrou p $N$\nto the function field of a maximal torus. It is related to the geom etry of \nMirkovic-Vilonen cycles via the notion of equivariant multiplici ty. This morphism \nturns out to be useful for comparing good bases of the coordinate algebra \n$\\mathbb{C}[N]$. We will focus on comparing the va lues taken by $\\overline{D}$ on several distinguished elements of the Mir kovic-Vilonen basis and the dual canonical basis. For the latter one\,\nwe will use Kang-Kashiwara-Kim-Oh's monoidal categorification of the cluster \nstructure of the cluster structure of $\\mathbb{C}[N]$ via quiver Hecke algebras as well as\nrecent results by Kashiwara-Kim. This will lead us to an explicit description of\nthe images under $\\overline{D}$ of the flag minors of $\\mathbb{C}[N]$ as well as remarkable\nidentities between them. \n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/28 / END:VEVENT BEGIN:VEVENT SUMMARY:Markus Reineke (Bochum) DTSTART;VALUE=DATE-TIME:20201130T130000Z DTEND;VALUE=DATE-TIME:20201130T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/29 DESCRIPTION:Title: Wild quantum dilogarithm identities\nby Markus R eineke (Bochum) as part of Paris algebra seminar\n\n\nAbstract\nWe formula te and discuss "wild" analogues of the Fadeev-Kashaev identity for quantum dilogarithms. We review a general quiver setup\nfor such identities\, res ulting from wall-crossing formulas\, motivic Donaldson-Thomas invariants\, and the geometry of quiver moduli spaces. The quantum dilogarithm identit ies are then derived from special properties of representations of general ized Kronecker quivers.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/29 / END:VEVENT BEGIN:VEVENT SUMMARY:Manon Defosseux (Université de Paris) DTSTART;VALUE=DATE-TIME:20210111T130000Z DTEND;VALUE=DATE-TIME:20210111T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/30 DESCRIPTION:Title: Brownian motion in the unit interval and the Littelm ann path model\nby Manon Defosseux (Université de Paris) as part of P aris algebra seminar\n\n\nAbstract\nWe will present for a Brownian motion in the unit interval a Pitman type\ntheorem obtained recently in joint wor k with Philippe Bougerol. We will focus\non algebraic aspects and will exp lain how it is related to the Littelmann path\nmodel for an affine Kac–M oody algebra of extended type $A_1$.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/30 / END:VEVENT BEGIN:VEVENT SUMMARY:Estanislao Herscovich (Grenoble) DTSTART;VALUE=DATE-TIME:20210118T130000Z DTEND;VALUE=DATE-TIME:20210118T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/31 DESCRIPTION:Title: Double quasi-Poisson algebras are pre-Calabi-Yau \nby Estanislao Herscovich (Grenoble) as part of Paris algebra seminar\n\n \nAbstract\nDouble Poisson and double quasi-Poisson algebras were introduc ed by M. Van den Bergh in his study of noncommutative quasi-Poisson geomet ry. Namely\, they satisfy the so-called Kontsevich-Rosenberg principle\, s ince the representation scheme of a double (quasi-)Poisson algebra has a n atural (quasi-)Poisson structure. On the other hand\, N. Iyudu and M. Kont sevich found a link between double Poisson algebras and pre-Calabi-Yau alg ebras\, a notion introduced by Kontsevich and Y. Vlassopoulos. The aim of this talk will be to explain how such a connection can be extended to doub le quasi-Poisson algebras\, which thus give rise to pre-Calabi-Yau algebra s. This pre-Calabi-Yau structure is however more involved in the case of d ouble quasi-Poisson algebras since\, in particular\, we get an infinite nu mber of nonvanishing higher multiplications for the associated pre-Calabi- Yau algebra\, which involve the Bernoulli numbers. \n\nThis is joint work with D. Fernández from the Universität Bielefeld.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/31 / END:VEVENT BEGIN:VEVENT SUMMARY:Emmanuel Letellier (Université de Paris) DTSTART;VALUE=DATE-TIME:20201214T130000Z DTEND;VALUE=DATE-TIME:20201214T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/32 DESCRIPTION:Title: E-series of character varieties associated with non orientable surfaces\nby Emmanuel Letellier (Université de Paris) as p art of Paris algebra seminar\n\n\nAbstract\nIn this talk we will be intere sted in two kinds of character varieties associated to a compact non-orien table surface S. The first one is just the quotient stack of all represent ations of the fundamental group of S in GL(n\,C). For the second one\, we consider k punctures of S as well as k semisimple conjugacy classes of GL( n\,C). We then consider the stack of anti-invariant local systems on the orientation covering of S with local monodromies around the punctures in t he prescribed conjugacy classes. We compute the number of points of these spaces over finite fields and we give a cohomological interpretation of ou r counting formulas. For the second kind of character varieties\, we give a conjectural formula for the mixed Poincaré series in terms of Macdonald symmetric functions.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/32 / END:VEVENT BEGIN:VEVENT SUMMARY:Ruslan Maksimau (Montpellier) DTSTART;VALUE=DATE-TIME:20201207T130000Z DTEND;VALUE=DATE-TIME:20201207T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/33 DESCRIPTION:Title: KLR algebras for curves and semi-cuspidal representa tions\nby Ruslan Maksimau (Montpellier) as part of Paris algebra semin ar\n\n\nAbstract\nThe talk is based on the preprint arXiv:2010.01419. This is joint work with Alexandre Minets.\n\nThe KLR algebras (also called qui ver Hecke algebras) are known to have the following geometric construction : they are isomorphic to the (equivariant) Borel-Moore homology of the Ste inberg variety. A point of this variety is given by a representation of a quiver and two full flags of subrepresentations.\n\nWe define and study an alogues of KLR algebras for curves (curve Hecke algebras). We define these algebras geometrically\, similarly to usual KLR algebras. But we replace representations of a quiver by torsion sheaves on a smooth curve C. In par ticular\, for C=P1\, we get a geometric realization of the affine zigzag a lgebra of type A1. The case C=P1 is particularly interesting because it al lows us to describe the imaginary semi-cuspidal category for the KLR algeb ra for affine sl2.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/33 / END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Lebed (Caen) DTSTART;VALUE=DATE-TIME:20210125T130000Z DTEND;VALUE=DATE-TIME:20210125T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/34 DESCRIPTION:Title: Homotopical tools for computing rack homology\nb y Victoria Lebed (Caen) as part of Paris algebra seminar\n\n\nAbstract\nRa cks are certain algebraic structures yielding powerful tools for knot theo ry\, Hopf algebra classification and other areas. Rack homology plays a cr ucial role in these applications. The homology of a rack is very easy to d efine (via an explicit chain complex)\, but extremely difficult to compute . Until recently\, the full homology was known only for three families of racks. Together with Markus Szymik\, we added a forth family to this list\ , the family of permutation racks. More importantly\, our work unexpectedl y brought homotopical methods into the area\, and showed that in spite of their abstract flavour they can yield concrete computations. The necessary background on racks and their homology\, as well as an overview of the to ols previously used for its computation\, will be given.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/34 / END:VEVENT BEGIN:VEVENT SUMMARY:Amnon Yekutieli (Ben Gurion University) DTSTART;VALUE=DATE-TIME:20210301T130000Z DTEND;VALUE=DATE-TIME:20210301T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/35 DESCRIPTION:Title: Rigidity\, Residues and Duality: Overview and Recent Progress\nby Amnon Yekutieli (Ben Gurion University) as part of Paris algebra seminar\n\n\nAbstract\nIn this lecture\, we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry. Un like all previous approaches to Grothendieck Duality\, the rigid approach concentrates on rigid residue complexes over rings\, and their intricate y et robust properties. Most of the lecture will about the results for rings . The geometrization\, i.e. the passage to rigid residue complexes on sche mes and Deligne-Mumford (DM) stacks\, by gluing\, is fairly easy. In the g eometric part of the theory\, the main results are the Rigid Residue Theor em and the Rigid Duality Theorem for proper maps between schemes\, and for tame proper maps between DM stacks. These results will only be outlined b riefly. \n\nMore details are available in the eprint with the same title a t\nhttps://arxiv.org/abs/2102.00255\n\nThe lecture notes can be downloaded from \nhttp://www.math.bgu.ac.il/~amyekut/lectures/RRD-2021/notes.pdf\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/35 / END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Tamaroff (Dublin) DTSTART;VALUE=DATE-TIME:20210201T130000Z DTEND;VALUE=DATE-TIME:20210201T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/36 DESCRIPTION:Title: Poincaré--Birkhoff--Witt theorems: homotopical and effective computational methods for universal envelopes\nby Pedro Tama roff (Dublin) as part of Paris algebra seminar\n\n\nAbstract\nIn joint wor k with V. Dotsenko\, we developed a categorical framework for Poincaré-Bi rkhoff-Witt type theorems about universal enveloping algebras of various a lgebraic structures\, and used methods of term rewriting for operads to ob tain new PBW theorems\, in particular answering an open question of J.-L. Loday. Later\, in joint work with A. Khoroshkin\, we developed a formalism to study Poincaré–Birkhoff–Witt type theorems for universal envelope s of algebras over differential graded operads\, motivated by the problem of computing the universal enveloping algebra functor on dg Lie algebras i n the homotopy category. Our formalism allows us\, among other things\, to obtain a homotopy invariant version of the classical Poincaré–Birkhoff –Witt theorem for universal envelopes of Lie algebras\, and extend Quill en's quasi-isomorphism C(g) ---> BU(g) to homotopy Lie algebras. I will su rvey and explain the role homological algebra\, homotopical algebra\, and effective computational methods play in the main results obtained with bot h V. Dotsenko (1804.06485) and A. Khoroshikin (2003.06055) and\, if time a llows\, explain a new direction in which these methods can be used to stud y certain operads as universal envelopes of pre-Lie algebras.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/36 / END:VEVENT BEGIN:VEVENT SUMMARY:Deniz Kus (Bochum) DTSTART;VALUE=DATE-TIME:20210315T130000Z DTEND;VALUE=DATE-TIME:20210315T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/37 DESCRIPTION:Title: Prime representations in the Hernandez-Leclerc categ ory\nby Deniz Kus (Bochum) as part of Paris algebra seminar\n\n\nAbstr act\nGenerators and relations of graded limits of certain finite dimension al irreducible representations of quantum affine algebras have been determ ined in recent years. For example\, the representations in the Hernandez-L eclerc category corresponding to cluster variables appear to be certain tr uncations of representations for current algebras and tensor products are related to the notion of fusion products. In this talk we will discuss som e known results on this topic and study the classical and graded character s of prime representations in the HL category.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/37 / END:VEVENT BEGIN:VEVENT SUMMARY:Milen Yakimov (Northeastern) DTSTART;VALUE=DATE-TIME:20210215T130000Z DTEND;VALUE=DATE-TIME:20210215T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/38 DESCRIPTION:Title: Root of unity quantum cluster algebras\nby Milen Yakimov (Northeastern) as part of Paris algebra seminar\n\n\nAbstract\nWe will describe a theory of root of unity quantum cluster algebras\, which are not necessarily specializations of quantum cluster algebras. All such algebras are shown to be polynomial identity (PI) algebras. Inside each of them\, we construct a canonical central subalgebra which is proved to be isomorphic to the underlying cluster algebra. (In turn\, this is used to s how that two exchange graphs are canonically isomorphic). This setting gen eralizes the De Concini-Kac-Procesi central subalgebras in big quantum gro ups and presents a general framework for studying the representation theor y of quantum algebras at roots of unity by means of cluster algebras as th e relevant data becomes (PI algebra\, canonical central subalgebra)=(root of unity quantum cluster algebra\, underlying cluster algebra). We also ob tain a formula for the corresponding discriminant in this general setting that can be applied in many concrete situations of interest\, such as the discriminants of all root of unity quantum unipotent cells for symmetrizab le Kac-Moody algebras\, defined integrally over Z[root of unity]. This is a joint work with Bach Nguyen (Xavier Univ) and Kurt Trampel (Notre Dame U niv).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/38 / END:VEVENT BEGIN:VEVENT SUMMARY:Sondre Kvamme (Uppsala) DTSTART;VALUE=DATE-TIME:20210208T130000Z DTEND;VALUE=DATE-TIME:20210208T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/39 DESCRIPTION:Title: Admissibly finitely presented functors for exact cat egories\nby Sondre Kvamme (Uppsala) as part of Paris algebra seminar\n \n\nAbstract\nIn this talk we introduce the category of admissibly finitel y presented functors mod_{adm}(E) for an exact category E. In particular\ , we characterize exact categories of the form mod_{adm}(E)\, and show tha t they have properties similar to module categories of Auslander algebras. For a fixed idempotent complete category C\, we also use this constructio n to show that exact structures on C correspond to certain resolving subca tegories in mod(C). This is joint work with Ruben Henrard and Adam-Christi aan van Roosmalen.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/39 / END:VEVENT BEGIN:VEVENT SUMMARY:Ryo Fujita (University of Paris) DTSTART;VALUE=DATE-TIME:20210308T130000Z DTEND;VALUE=DATE-TIME:20210308T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/40 DESCRIPTION:Title: Isomorphisms among quantum Grothendieck rings and pr opagation of positivity\nby Ryo Fujita (University of Paris) as part o f Paris algebra seminar\n\n\nAbstract\nFor a complex simple Lie algebra $\ \mathfrak{g}$\, finite-dimensional representations of its quantum loop alg ebra form an interesting monoidal abelian category\, which has been studie d from various perspectives. Related to the fundamental problem of determi ning the characters of irreducible representations\, we consider its quant um Grothendieck ring\, a 1-parameter deformation of the usual Grothendieck ring. When $\\mathfrak{g}$ is of simply-laced type\, Nakajima and Varagno lo-Vasserot proved that it enjoys some positivity properties based on the geometry of quiver varieties. In this talk\, we show that the same positiv ities hold also for non-simply-laced type by establishing an isomorphism b etween the quantum Grothendieck ring of non-simply-laced type and that of ''unfolded'' simply-laced type. In addition\, we find that an analog of Ka zhdan-Lusztig conjecture holds for several new cases in non-simply-laced t ype. This is a joint work with David Hernandez\, Se-jin Oh\, and Hironori Oya.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/40 / END:VEVENT BEGIN:VEVENT SUMMARY:Alexander P. Veselov (Loughborough (UK) and Moscow (Russia)) DTSTART;VALUE=DATE-TIME:20210322T130000Z DTEND;VALUE=DATE-TIME:20210322T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/42 DESCRIPTION:Title: Automorphic Lie algebras and modular forms\nby A lexander P. Veselov (Loughborough (UK) and Moscow (Russia)) as part of Par is algebra seminar\n\n\nAbstract\nThe automorphic Lie algebras can be view ed as generalisations of twisted loop Lie algebras\, when a group $G$ acts holomorphically and discretely on a Riemann surface and by automorphisms on the chosen Lie algebra. \n \nIn the talk we will discuss the automorphi c Lie algebras of modular type\, when $G$ is a finite index subgroup of th e modular group $\\Gamma=SL(2\, \\mathbb Z)$ acting on the upper half pla ne. In the case when the action of $G$ can be extended to $SL(2\,\\mathbb C)$ we prove analogues of Kac’s isomorphism theorem for the twisted loop Lie algebras.\nFor the modular group and some of its principal congruence subgroups we provide an explicit description of such isomorphisms using t he classical theory of modular forms.\n \nThe talk is based on the ongoing joint work with Vincent Knibbeler and Sara Lombardo.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/42 / END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Ovsienko (Reims) DTSTART;VALUE=DATE-TIME:20210222T130000Z DTEND;VALUE=DATE-TIME:20210222T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/43 DESCRIPTION:Title: Combinatorial and analytic properties of q-deformed real numbers\nby Valentin Ovsienko (Reims) as part of Paris algebra s eminar\n\n\nAbstract\nI will explain a recent notion of \nq-deformed real numbers\, and discuss its various combinatorial and analytic properties. A "\nq-deformed real" is a Laurent series in one variable\, \nq\, with inte ger coefficients. The subject is connected to different theories\, such as knot invariants\, continued fractions\, and cluster algebras. I will form ulate a challenging conjecture about the convergence of the series arising as \nq-deformed real numbers. (Here we understand \nq as a complex variab le.) The conjecture is proved in particular cases and concrete examples. I n the most simple examples of q-Fibonacci and q-Pell numbers\, the explici t formulas for the radius of convergence are very similar to certain formu las of Ramanujan. \nThe talk is based on a joint work with Ludivine Lecler e\, Sophie Morier-Genoud and Alexander Veselov.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/43 / END:VEVENT BEGIN:VEVENT SUMMARY:Oleksandr Tsymbaliuk (Purdue) DTSTART;VALUE=DATE-TIME:20210503T120000Z DTEND;VALUE=DATE-TIME:20210503T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/44 DESCRIPTION:Title: Quantum loop groups and shuffle algebras via Lyndon words\nby Oleksandr Tsymbaliuk (Purdue) as part of Paris algebra semin ar\n\n\nAbstract\nClassical q-shuffle algebras provide combinatorial model s for the positive half U_q(n) of a finite quantum group. We define a loop version of this construction\, yielding a combinatorial model for the pos itive half U_q(Ln) of a quantum loop group. In particular\, we construct a PBW basis of U_q(Ln) indexed by standard Lyndon words\, generalizing the work of Lalonde-Ram\, Leclerc and Rosso in the U_q(n) case. We also connec t this to Enriquez' degeneration A of the elliptic algebras of Feigin-Odes skii\, proving a conjecture that describes the image of the embedding U_q( Ln) ---> A in terms of pole and wheel conditions. Joint work with Andrei N egut.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/44 / END:VEVENT BEGIN:VEVENT SUMMARY:Gregg Musiker (Minnesota) DTSTART;VALUE=DATE-TIME:20210426T120000Z DTEND;VALUE=DATE-TIME:20210426T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/45 DESCRIPTION:Title: Combinatorial Expansion Formulas for Decorated Super -Teichmüller Spaces\nby Gregg Musiker (Minnesota) as part of Paris al gebra seminar\n\n\nAbstract\nMotivated by the definition of super Teichmul ler spaces\, and Penner-Zeitlin's recent extension of this definition to d ecorated super Teichmuller space\, as examples of super Riemann surfaces\, we use the super Ptolemy relations to obtain formulas for super lambda-le ngths associated to arcs in a bordered surface. In the special case of a d isk\, we are able to give combinatorial expansion formulas for the super l ambda-lengths associated to diagonals of a polygon in the spirit of Ralf S chiffler's T-path formulas for type A cluster algebras. We further connect our formulas to the super-friezes of Morier-Genoud\, Ovsienko\, and Tabac hnikov\, and obtain partial progress towards defining super cluster algebr as of type A. In particular\, following Penner-Zeitlin\, we are able to ge t formulas (up to signs) for the mu-invariants associated to triangles in a triangulated polygon\, and explain how these provide a step towards unde rstanding odd variables of a super cluster algebra. This is joint work wi th Nicholas Ovenhouse and Sylvester Zhang.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/45 / END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Mozgovoy (Trinity College Dublin) DTSTART;VALUE=DATE-TIME:20210329T120000Z DTEND;VALUE=DATE-TIME:20210329T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/47 DESCRIPTION:Title: Operadic approach to wall-crossing and attractor inv ariants\nby Sergey Mozgovoy (Trinity College Dublin) as part of Paris algebra seminar\n\n\nAbstract\nWall-crossing describes how various invaria nts in algebraic geometry and theoretical physics transform under the vari ation of parameters. In this talk I will discuss a framework\, reminiscent of collections and plethysms in the theory of operads\, that concenptuali zes those transformation rules. I will describe how some new and existing wall-crossing formulas can be proved using this approach. In particular\, I will discuss applications to attractor invariants (also called initial d ata in the theory of scattering diagrams).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/47 / END:VEVENT BEGIN:VEVENT SUMMARY:Erik Darpoe (Nagoya) DTSTART;VALUE=DATE-TIME:20210412T120000Z DTEND;VALUE=DATE-TIME:20210412T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/48 DESCRIPTION:Title: Periodic trivial extension algebras and fractionally Calabi–Yau algebras\nby Erik Darpoe (Nagoya) as part of Paris algeb ra seminar\n\n\nAbstract\nAn important open problem in the homological alg ebra of self-injective algebras is to characterise periodic algebras. An a lgebra B is said to be periodic if if has a periodic projective resolution as a B-B-bimodule.\n\nIn this talk\, I will present a solution to this pr oblem for trivial extension algebras: the trivial extension algebra T(A) o f a finite-dimensional algebra A is periodic if and only if A has finite g lobal dimension and is fractionally Calabi-Yau.\n\nThis is based on joint work with Chan\, Iyama and Marczinzik.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/48 / END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Baumann (Strasbourg) DTSTART;VALUE=DATE-TIME:20210510T120000Z DTEND;VALUE=DATE-TIME:20210510T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/49 DESCRIPTION:Title: Explicit calculations in the geometric Satake equiva lence\nby Pierre Baumann (Strasbourg) as part of Paris algebra seminar \n\n\nAbstract\nLet $G$ be a complex connected reductive group. As shown b y Mirković and Vilonen\, the geometric Satake equivalence yields a basis in each irreducible rational representation of $G$\, defined out of algebr aic cycles in the affine Grassmannian of the Langlands dual of $G$. Goncha rov and Shen extended this construction to each tensor product of irreduci ble representations. We will investigate the properties of all these bases and explain a method to compute them. Based on a joint work with Peter Li ttelmann and Stéphane Gaussent.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/49 / END:VEVENT BEGIN:VEVENT SUMMARY:Damien Calaque (Montpellier) DTSTART;VALUE=DATE-TIME:20210531T120000Z DTEND;VALUE=DATE-TIME:20210531T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/50 DESCRIPTION:Title: Calabi-Yau structures for multiplicative preprojecti ve algebras\nby Damien Calaque (Montpellier) as part of Paris algebra seminar\n\n\nAbstract\nI will start by motivating and recalling Calabi-Yau structures and relative versions thereof. \nI will then provide several e xamples of Calabi-Yau structures occurring in the context of (dg-versions of) multiplicative preprojective algebras. The A_2 case\, that we will des cribe in detail\, will be used as a building block for general quivers. At the end of the talk\, I will describe a strategy for a comparison with ot her constructions\, for instance Van den Bergh's quasi-bi-hamiltonian stru ctures. \nThis is a report on joint work with Tristan Bozec and Sarah Sche rotzke.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/50 / END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Williams (Leicester) DTSTART;VALUE=DATE-TIME:20210419T120000Z DTEND;VALUE=DATE-TIME:20210419T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/51 DESCRIPTION:Title: The higher Stasheff–Tamari orders in representatio n theory\nby Nicholas Williams (Leicester) as part of Paris algebra se minar\n\n\nAbstract\nOppermann and Thomas show that tilting modules over I yama's higher Auslander algebras of type A are in bijection with triangula tions of even-dimensional cyclic polytopes. Triangulations of cyclic polyt opes are partially ordered in two natural ways known as the higher Stashef f–Tamari orders\, which were introduced in the 1990s by Kapranov\, Voevo dsky\, Edelman\, and Reiner as higher-dimensional generalisations of the T amari lattice. These two partial orders were conjectured to be equal in 19 96 by Edelman and Reiner\, but this is still an open problem. We show how the higher Stasheff–Tamari orders correspond in even dimensions to natur al orders on tilting modules which were studied by Riedtmann\, Schofield\, Happel\, and Unger. This then allows us to complete the picture of Opperm ann and Thomas by showing that triangulations of odd-dimensional cyclic po lytopes correspond to equivalence classes of d-maximal green sequences\, w hich we introduce as higher-dimensional analogues of Keller’s maximal gr een sequences. We show that the higher Stasheff–Tamari orders correspond to natural orders on equivalence classes of d-maximal green sequences\, w hich relate to the no-gap conjecture of Brüstle\, Dupont\, and Perotin. I f time permits\, we will also briefly discuss more recent work concerning the relation between the first higher Stasheff–Tamari orders and the hig her Bruhat orders\, which are higher-dimensional analogues of the weak Bru hat order on the symmetric group.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/51 / END:VEVENT BEGIN:VEVENT SUMMARY:Sachin Gautam (Ohio State) DTSTART;VALUE=DATE-TIME:20210517T120000Z DTEND;VALUE=DATE-TIME:20210517T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/52 DESCRIPTION:Title: Poles of finite-dimensional representations of Yangi ans\nby Sachin Gautam (Ohio State) as part of Paris algebra seminar\n\ n\nAbstract\nThe Yangian associated to a simple Lie algebra g is a Hopf al gebra which quantizes the Lie algebra of polynomials g[t]. Its finite-dime nsional representation theory has remarkable connections with equivariant cohomology\, combinatorics\, integrable systems and mathematical physics. Concretely\, a finite-dimensional representation of the Yangian is prescri bed by a finite collection of operators whose coefficients are rational fu nctions\, satisfying a list of commutation relations.\n\nIn this talk I wi ll give an explicit combinatorial description of the sets of poles of the rational currents of the Yangian\, acting on an irreducible finite-dimensi onal representation. This result uses the generalization of Baxter's Q-ope rators obtained by Frenkel-Hernandez. Based on a joint work with Curtis We ndlandt (arxiv:2009.06427).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/52 / END:VEVENT BEGIN:VEVENT SUMMARY:Justine Fasquel (Lille) DTSTART;VALUE=DATE-TIME:20210614T120000Z DTEND;VALUE=DATE-TIME:20210614T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/53 DESCRIPTION:Title: Rationality at admissible levels of the simple W-alg ebras associated with subregular nilpotent elements in sp_4\nby Justin e Fasquel (Lille) as part of Paris algebra seminar\n\n\nAbstract\nW-algebr as are certain vertex algebras obtained from the quantized Drinfeld-Sokolo v reduction of universal affine vertex algebras associated with a complex parameter k and a simple complex Lie algebra g. Their simple quotients are believed to be rational for specific values of k\, called admissible\, wh ich depend on the choice of a nilpotent orbit in g. Here\, by rationality\ , one means the complete reducibility of their positively graded modules.\ n\nThis conjecture was partially proved by Arakawa-van Ekeren and Creutzig -Linshaw. In this talk\, I will discuss some consequences of the rationali ty for a very concrete example\, namely the W-algebra associated with a su bregular nilpotent element of the symplectic Lie algebra sp_4. In particul ar\, we will be interested in certain actions on the W-algebra and the set of its simple modules.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/53 / END:VEVENT BEGIN:VEVENT SUMMARY:Dan Kaplan (Birmingham) DTSTART;VALUE=DATE-TIME:20210524T120000Z DTEND;VALUE=DATE-TIME:20210524T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/54 DESCRIPTION:Title: Multiplicative preprojective algebras for Dynkin qui vers\nby Dan Kaplan (Birmingham) as part of Paris algebra seminar\n\n\ nAbstract\nCrawley-Boevey and Shaw defined the multiplicative preprojectiv e algebra to understand Kac’s middle convolution and to solve the Delign e-Simpson problem. In Shaw’s thesis he noticed a curious phenomenon: for the D_4 quiver the multiplicative preprojective algebra (with parameter q =1) is isomorphic to the (additive) preprojective algebra if and only if t he underlying field has characteristic not two. Later\, Crawley-Boevey pro ved the multiplicative and additive preprojective algebras are isomorphic for all Dynkin quivers over the complex numbers. Recent work of Etgü-Leki li and Lekili-Ueda\, in the dg-setting\, sharpens the result to hold over fields of good characteristic\, meaning characteristic not 2 in type D\, n ot 2 or 3 in type E and not 2\, 3\, or 5 for E_8. Neither work produces an isomorphism. \n\nIn this talk\, I will explain how to construct these iso morphisms and prove their non-existence in the bad (i.e.\, not good) chara cteristics. For each bad characteristic\, a single class in zeroth Hochsch ild homology obstructs the existence of an isomorphism. Time permitting\, I’ll explain how to interpret these results in the dg-setting where the 2-Calabi-Yau property allows us to recast these obstructions as non-trivia l deformations\, using Van den Bergh duality.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/54 / END:VEVENT BEGIN:VEVENT SUMMARY:Pierrick Bousseau (Orsay) DTSTART;VALUE=DATE-TIME:20210607T120000Z DTEND;VALUE=DATE-TIME:20210607T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/55 DESCRIPTION:Title: The flow tree formula for Donaldson-Thomas invariant s of quivers with potentials\nby Pierrick Bousseau (Orsay) as part of Paris algebra seminar\n\n\nAbstract\nVery generally\, Donaldson-Thomas inv ariants are counts of stable objects in Calabi-Yau triangulated categories of dimension 3. A natural source of examples is provided by the represent ation theory of quivers with potentials. I will present a proof of a formu la\, conjectured by Alexandrov-Pioline from string-theory arguments\, whic h computes Donaldson-Thomas invariants of a quiver with potential in terms of a much smaller set of "attractor invariants". The proof uses the frame work of scattering diagrams to reorganize sequences of iterated applicatio ns of the Kontsevich-Soibelman wall-crossing formula. This is joint work w ith Hülya Argüz.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/55 / END:VEVENT BEGIN:VEVENT SUMMARY:Shunsuke Kano (Tōhoku) DTSTART;VALUE=DATE-TIME:20210621T120000Z DTEND;VALUE=DATE-TIME:20210621T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/56 DESCRIPTION:Title: Categorical dynamical systems arising from sign-stab le mutation loops\nby Shunsuke Kano (Tōhoku) as part of Paris algebra seminar\n\n\nAbstract\nA pair formed by a triangulated category and an au toequivalence is called a \ncategorical dynamical system. Its complexity i s measured by the so-called categorical entropy. \nIn this talk\, I will p resent a computation of the categorical entropies of categorical dynamical systems obtained by lifting a sign-stable mutation loop of a quiver to an autoequivalence of the derived category of the corresponding Ginzburg dg algebra.\nThe notion of sign-stability is introduced as a generalization o f the pseudo-Anosov property of mapping classes of surfaces. If time permi ts\, we will discuss the pseudo-Anosovness of the autoequivalences constru cted.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/56 / END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Gorsky (Amiens) DTSTART;VALUE=DATE-TIME:20210628T120000Z DTEND;VALUE=DATE-TIME:20210628T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/57 DESCRIPTION:Title: Braid varieties\, positroids\, and Legendrian links< /a>\nby Mikhail Gorsky (Amiens) as part of Paris algebra seminar\n\n\nAbst ract\nI will discuss a class of affine algebraic varieties associated with positive braids\, their cluster structures and their relation to open Bot t-Samelson varieties. First\, I will explain our motivation which comes bo th from symplectic topology and from the study of HOMFLY-PT polynomials. T hen we will discuss how the study of DG algebras associated with certain L egendrian links may help us to better understand the algebraic geometry of Richardson varieties in type A. I will illustrate our results and conject ures concerning this interplay between topology and algebraic geometry wit h the example of open positroid varieties in Grassmannians. If time permit s\, I will briefly explain conjectural relations between certain stratific ations of braid varieties and cluster structures on their coordinate rings . This is joint work with Roger Casals\, Eugene Gorsky\, and José Simenta l.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/57 / END:VEVENT BEGIN:VEVENT SUMMARY:Ehud Meir (Aberdeen) DTSTART;VALUE=DATE-TIME:20210705T120000Z DTEND;VALUE=DATE-TIME:20210705T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/58 DESCRIPTION:Title: Interpolations of monoidal categories by invariant t heory\nby Ehud Meir (Aberdeen) as part of Paris algebra seminar\n\n\nA bstract\nIn this talk\, I will present a recent construction that enables one to\ninterpolate symmetric monoidal categories by interpolating algebra ic\nstructures and their automorphism groups.\nI will explain how one can recover the constructions of Deligne for\ncategories such as Rep(S_t)\, Re p(O_t) and Rep(Sp_t)\, the constructions\nof Knop for wreath products with S_t and GL_t(O_r)\, where O_r is a\nfinite quotient of a discrete valuati on ring\, and also the TQFT\ncategories recently constructed from a ration al function by Khovanov\, Ostrik\, and Kononov.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/58 / END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Cerulli Irelli (Rome La Sapienza) DTSTART;VALUE=DATE-TIME:20211004T120000Z DTEND;VALUE=DATE-TIME:20211004T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/59 DESCRIPTION:Title: On degeneration and extensions of symplectic and ort hogonal quiver representations\nby Giovanni Cerulli Irelli (Rome La Sa pienza) as part of Paris algebra seminar\n\n\nAbstract\nMotivated by linea r degenerations of flag varieties\, and the study of 2-nilpotent B-orbits for classical groups\, I will review the representation theory of symmetri c quivers\, initiated by Derksen and Weyman in 2002. I will then focus on the problem of describing the orbit closures in this context and how to re late it to the orbit closures for the underlying quivers. In collaboration with M. Boos we have recently given an answer to this problem for symmetr ic quivers of finite type. I believe that this result is a very special ca se of a much deeper and general result that I will mention in the form of conjectures and open problems. The talk is based on the preprint version o f my paper with Boos available on the arXiv as 2106.08666.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/59 / END:VEVENT BEGIN:VEVENT SUMMARY:Maxim Gurevich (Technion\, Haifa) DTSTART;VALUE=DATE-TIME:20211011T120000Z DTEND;VALUE=DATE-TIME:20211011T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/60 DESCRIPTION:Title: RSK-transform for L-parameters\nby Maxim Gurevic h (Technion\, Haifa) as part of Paris algebra seminar\n\nAbstract: TBA\n\n What is common between the Specht construction for modules over\npermutati on groups\, normal sequences of quiver Hecke algebra modules à\nla Kashiw ara-Kim\, and the local Langlands classification for GL_n ?\nI would like to show how these themes fit well together under a\nframework of a represe ntation-theoretic Robinson-Schensted-Knuth\ntransform\, devised recently i n my work with Erez Lapid on\nrepresentations of p-adic groups.\n\nOn one hand\, RSK-standard modules are curious models for all smooth\nirreducible GL_n-representations. Yet\, going through Bernstein-Rouquier\ncategorical equivalences this notion is quantized into its natural\nexistence in the realm of type A quiver Hecke algebras. A convenient\nbridge is thus portra yed between the cyclotomic approach of classifying\nsimple modules through a generalized Specht construction\, and the\nPBW-basis approach from Lusz tig's work on quantum groups.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/60 / END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Pressland (Leeds) DTSTART;VALUE=DATE-TIME:20211018T120000Z DTEND;VALUE=DATE-TIME:20211018T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/63 DESCRIPTION:Title: A cluster character for y-variables\nby Matthew Pressland (Leeds) as part of Paris algebra seminar\n\n\nAbstract\nGiven a (Frobenius or triangulated) cluster category\, I will explain how to categ orify various cluster algebraic identities via lattice maps associated to pairs of cluster-tilting objects. For example\, one such map is the index\ , well-known to categorify g-vectors. Using this formalism\, I will recall the cluster character for x-variables developed by Caldero–Chapoton\, P alu\, Fu–Keller and others\, and give a similar categorical expression f or y-variables. This is joint work with Jan E. Grabowski.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/63 / END:VEVENT BEGIN:VEVENT SUMMARY:Haicheng Zhang (Nanjing Normal University) DTSTART;VALUE=DATE-TIME:20211108T130000Z DTEND;VALUE=DATE-TIME:20211108T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/66 DESCRIPTION:Title: Hall algebras of extriangulated categories and quant um cluster algebras\nby Haicheng Zhang (Nanjing Normal University) as part of Paris algebra seminar\n\n\nAbstract\nFirstly\, we define the Hall algebra of an extriangulated category\, a notion introduced by Nakaoka an d Palu. Then for a finite acyclic valued quiver Q\, we consider the Hall a lgebras of certain subcategories of the bounded derived category of the re presentation category of Q over a finite field\, which are extriangulated categories. We recover the quantum Caldero-Chapoton formula via the Hall a lgebra approach and give the higher-dimensional (cluster) multiplication f ormulas in the quantum cluster algebra of Q with arbitrary coefficients\, which can be viewed as the quantum version of the Caldero-Keller multiplic ation formula in the cluster algebra. This talk is based on the joint prep rints arXiv:2005.10617\, 2107.05883 and 2108.03558.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/66 / END:VEVENT BEGIN:VEVENT SUMMARY:Ryo Fujita (University of Paris) DTSTART;VALUE=DATE-TIME:20211122T130000Z DTEND;VALUE=DATE-TIME:20211122T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/67 DESCRIPTION:Title: Deformed Cartan matrices and generalized preprojecti ve algebras\, II\nby Ryo Fujita (University of Paris) as part of Paris algebra seminar\n\n\nAbstract\nIn their study of deformed W-algebras asso ciated with complex simple Lie algebras\, E. Frenkel-Reshetikhin (1998) in troduced certain two parameter deformations of the Cartan matrices. They p lay an important role in the representation theory of quantum affine algeb ras. In the former half of this talk\, we explain a representation-theoret ic interpretation of these deformed Cartan matrices and their inverses in terms of the generalized preprojective algebras recently introduced by Gei ss-Leclerc-Schröer (2017). In the latter half of the talk\, we discuss it s application to the representation theory of quantum affine algebras in c onnection with the theory of cluster algebras.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/67 / END:VEVENT BEGIN:VEVENT SUMMARY:Kota Murakami (Kyoto) DTSTART;VALUE=DATE-TIME:20211122T130000Z DTEND;VALUE=DATE-TIME:20211122T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/68 DESCRIPTION:Title: Deformed Cartan matrices and generalized preprojecti ve algebras\, I\nby Kota Murakami (Kyoto) as part of Paris algebra sem inar\n\n\nAbstract\nIn their study of deformed W-algebras associated with complex simple Lie algebras\, E. Frenkel-Reshetikhin (1998) introduced cer tain two parameter deformations of the Cartan matrices. They play an impor tant role in the representation theory of quantum affine algebras. In the former half of this talk\, we explain a representation-theoretic interpret ation of these deformed Cartan matrices and their inverses in terms of the generalized preprojective algebras recently introduced by Geiss-Leclerc-S chröer (2017). In the latter half of the talk\, we discuss its applicatio n to the representation theory of quantum affine algebras in connection wi th the theory of cluster algebras.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/68 / END:VEVENT BEGIN:VEVENT SUMMARY:Lucien Hennecart (Edinburgh) DTSTART;VALUE=DATE-TIME:20211025T120000Z DTEND;VALUE=DATE-TIME:20211025T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/69 DESCRIPTION:Title: (Canonical) bases of the elliptic Hall algebra\n by Lucien Hennecart (Edinburgh) as part of Paris algebra seminar\n\n\nAbst ract\nThe global nilpotent cone is a closed substack of the stack of Higgs sheaves on a smooth projective curve whose geometry has been studied in d epth and is also an essential object in the geometric Langlands program. I t is a highly singular stack and in particular it has several irreducible components which were rather recently explicitly described by Bozec. In th is talk\, we will concentrate on elliptic curves. We will recall Bozec's p arametrization of the set of irreducible components of the global nilpoten t cone and present another parametrization of the same set using (a refine ment of) the Harder-Narasimhan stratification of the stack of coherent she aves on the elliptic curve. Then\, we raise the question of the comparison of these two bases\, showing the emergence piecewise linear structures. W e will also see how the second description can be useful to understand a p art of the cohomological Hall algebra of an elliptic curve.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/69 / END:VEVENT BEGIN:VEVENT SUMMARY:Michael Wemyss (Edinburgh) DTSTART;VALUE=DATE-TIME:20220131T130000Z DTEND;VALUE=DATE-TIME:20220131T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/70 DESCRIPTION:Title: Local Normal Forms of Noncommutative Functions\n by Michael Wemyss (Edinburgh) as part of Paris algebra seminar\n\n\nAbstra ct\nThis talk will explain how to generalise Arnold's results classifying commutative singularities into the noncommutative setting\, and will class ify finite dimensional Jacobi algebras arising on the d-loop quiver. The surprising thing is that a classification should exist at all\, and it is even more surprising that ADE enters. I will spend most of my time explai ning what the algebras are\, why they classify\, and how to intrinsically extract ADE information from them. At the end\, I'll briefly explain why I 'm really interested in this problem\, the connection with different quive rs\, and the applications of the above classification to curve counting an d birational geometry. This is all joint work with Gavin Brown.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/70 / END:VEVENT BEGIN:VEVENT SUMMARY:Lang Mou (Cambridge) DTSTART;VALUE=DATE-TIME:20211115T130000Z DTEND;VALUE=DATE-TIME:20211115T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/71 DESCRIPTION:Title: Generalized cluster dualities\nby Lang Mou (Camb ridge) as part of Paris algebra seminar\n\n\nAbstract\nFock and Goncharov introduced dualities between cluster varieties. I will explain how this du ality under the framework of Gross-Hacking-Keel-Kontsevich can be naturall y extended to generalized cluster varieties in the sense of Chekhov-Shapir o. In particular\, I will construct generalized cluster scattering diagram s which are used to construct bases of functions on the dual varieties. As a generalized A-cluster variety yields a generalized cluster algebra\, ce rtain positivity property of the cluster monomials will be derived as a re sult of the positivity of the corresponding scattering diagram. This talk is mainly based on arXiv: 2110.02416.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/71 / END:VEVENT BEGIN:VEVENT SUMMARY:Chris Fraser (Minnesota) DTSTART;VALUE=DATE-TIME:20211129T130000Z DTEND;VALUE=DATE-TIME:20211129T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/72 DESCRIPTION:Title: Automorphisms of open positroid varieties from braid s\nby Chris Fraser (Minnesota) as part of Paris algebra seminar\n\n\nA bstract\nPositroid varieties are distinguished subvarieties of Grassmannia ns which have cluster structure(s). I will give some reminders on the comb inatorics underlying these cluster structures\, partially based on a joint work with Melissa Sherman-Bennett. In a previous work\, I described an ac tion of a certain braid group on the top-dimensional positroid subvariety by "quasi" cluster automorphisms. I will explain how a similar statement c an be extended to arbitrary open positroid varieties. This is joint with B ernhard Keller.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/72 / END:VEVENT BEGIN:VEVENT SUMMARY:Abel Lacabanne (Clermont-Ferrand) DTSTART;VALUE=DATE-TIME:20211213T130000Z DTEND;VALUE=DATE-TIME:20211213T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/73 DESCRIPTION:Title: Higher rank Askey-Wilson algebras as skein algebras< /a>\nby Abel Lacabanne (Clermont-Ferrand) as part of Paris algebra seminar \n\n\nAbstract\nThe skein algebra of a surface is built from the framed un oriented links in the thickened surface\, modulo the Kauffman bracket rela tions. If the surface is the $4$-punctured sphere\, it turns out that the skein algebra is a central extension of the universal Askey-Wilson algebra . De Bie\, De Clercq and Van de Vijver proposed a definition of higher ran k Askey-Wilson algebras\, as a subalgebra of an $n$-fold tensor product of $U_q(\\mathfrak{sl}_2)$. The aim of this talk is to explain an isomorphis m between these higher rank Askey-Wilson algebras\, and the skein algebras of punctured spheres. The diagrammatic flavour of the skein algebra provi des then an efficient way to compute some relations between some elements of the Askey-Wilson algebra\, notably the $q$-commutation relations discov ered by De Clercq. This is joint work with J. Cooke.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/73 / END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Ovenhouse (Minnesota) DTSTART;VALUE=DATE-TIME:20211206T130000Z DTEND;VALUE=DATE-TIME:20211206T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/74 DESCRIPTION:Title: q-Rational Numbers and Finite Schubert Varieties \nby Nicholas Ovenhouse (Minnesota) as part of Paris algebra seminar\n\n\n Abstract\nRecently\, Morier-Genoud and Ovsienko generalized the notion of q-integers to include rational numbers. The q-analogue of a rational numbe r is some rational function with integer coefficients. There are some know n combinatorial interpretations of the numerators as rank generating funct ions of certain posets. I will review this interpretation\, and re-phrase it in terms of lattice paths on "snake graphs". Using this snake graph int erpretation\, I will explain how the numerators count the number of points in some variety over a finite field. This variety is a union of Schubert cells in some Grassmannian.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/74 / END:VEVENT BEGIN:VEVENT SUMMARY:Alfredo Nájera Chávez (Oaxaca) DTSTART;VALUE=DATE-TIME:20220117T130000Z DTEND;VALUE=DATE-TIME:20220117T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/75 DESCRIPTION:Title: Deformation theory for finite cluster complexes\ nby Alfredo Nájera Chávez (Oaxaca) as part of Paris algebra seminar\n\n\ nAbstract\nCluster complexes are a certain class of simplicial complexes t hat naturally arise in the theory of cluster algebras. They codify a wealt h of fundamental information about cluster algebras. The purpose of this t alk is to elaborate on a geometric relationship between cluster algebras a nd cluster complexes. In vague words\, this relationship is the following: cluster algebras of finite cluster type with universal coefficients may b e obtained via a torus action on a Hilbert scheme. In particular\, we will discuss the deformation theory of the Stanley-Reisner ring associated to a finite cluster complex and present some applications related to the Grö bner theory of the ideal of relations among cluster and frozen variables o f a cluster algebra of finite cluster type. Time permitting I will elabora te on how to generalize this approach to the context of tau-tilting finite algebras.\n\nThis is based on a joint project with Nathan Ilten and Hipol ito Treffinger whose first outcome is the preprint arXiv:2111.02566.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/75 / END:VEVENT BEGIN:VEVENT SUMMARY:Merlin Christ (Hamburg) DTSTART;VALUE=DATE-TIME:20220124T130000Z DTEND;VALUE=DATE-TIME:20220124T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/76 DESCRIPTION:Title: Gluing constructions of Ginzburg algebras and cluste r categories\nby Merlin Christ (Hamburg) as part of Paris algebra semi nar\n\n\nAbstract\nGinzburg algebras are a class of 3-CY dg algebras\, whi ch have attracted attention for their use in the categorification of clust er algebras. Given a marked surface with a triangulation\, there is an ass ociated Ginzburg algebra G. I will begin by describing how its derived cat egory D^perf(G) can be glued from the derived categories of the relative G inzburg algebras of the ideal triangles of the triangulation. We will see that the passage to Amiot's cluster category\, defined as the quotient D^p erf(G)/D^fin(G)\, does not commute with this gluing. As we will discuss\, this can fixed by instead starting with the relative Ginzburg algebra of t he triangulation and again applying Amiot's quotient formula. Remarkably\, this resulting relative version of cluster category turns out to be equiv alent to the 1-periodic topological Fukaya category of the surface.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/76 / END:VEVENT BEGIN:VEVENT SUMMARY:Chris Brav (HSE Moscow) DTSTART;VALUE=DATE-TIME:20220110T130000Z DTEND;VALUE=DATE-TIME:20220110T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/77 DESCRIPTION:Title: Non-commutative string topology\nby Chris Brav ( HSE Moscow) as part of Paris algebra seminar\n\n\nAbstract\nWe explain how relative Calabi-Yau structures on dg functors\, more generally relative o rientations\, give a non-commutative generalisation of oriented manifolds with boundary. We then construct genus zero string topology operations on the relative Hochschild homology HH_*(C\,D) of a dg functor D —> C equip ped with a relative orientation. More precisely\, we prove a relative vers ion of the cyclic Deligne conjecture\, stating that this shifted relative Hochschild homology carries a natural structure of framed E_2-algebra. Exa mples include 1) the functor of induction of local systems for the inclusi on of the boundary into an oriented manifold with boundary\, in which case the relative Hochschild homology is identified with the relative loop hom ology 2) the functor of pushforward of coherent sheaves for the inclusion of the anti-canonical divisor into a variety\, in which case relative Hoch schild homology can be related to differential forms\, and 3) various exam ples coming from representation theory.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/77 / END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Williams (Cologne) DTSTART;VALUE=DATE-TIME:20220207T130000Z DTEND;VALUE=DATE-TIME:20220207T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/78 DESCRIPTION:Title: Equivalence of maximal green sequences\nby Nicho las Williams (Cologne) as part of Paris algebra seminar\n\n\nAbstract\nIt is natural to study the set of maximal green sequences of an algebra under an equivalence relation. The resulting set of equivalence classes has the structure of a poset\; it is a lattice in type A\, where the equivalence classes are in bijection with triangulations of three-dimensional cyclic p olytopes. There are at least four appealing ways of defining an equivalenc e relation on maximal green sequences: commutation\, exchange pairs\, tau- rigid summands\, and bricks. The main result of my talk will be that the f irst three methods define the same equivalence relation\, while the fourth does not. This gives a surprising lack of duality between bricks\, which correspond to simples\, and tau-rigid summands\, which correspond to proje ctives. This is a report on joint work in progress with Mikhail Gorsky.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/78 / END:VEVENT BEGIN:VEVENT SUMMARY:Véronique Bazier-Matte (Connecticut) DTSTART;VALUE=DATE-TIME:20220214T130000Z DTEND;VALUE=DATE-TIME:20220214T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/79 DESCRIPTION:Title: Connection between knot theory and Jacobian algebras \nby Véronique Bazier-Matte (Connecticut) as part of Paris algebra se minar\n\n\nAbstract\nThis is joint work with Ralf Schiffler.\nIn knot theo ry\, it is known that we can compute the Alexander polynomial of a knot fr om the lattice of Kauffman states of a knot diagram. Recently\, my collabo rator and I associated a quiver with a knot diagram. From this quiver\, on e can obtain a Jacobian algebra. It appears that the lattice of submodules of indecomposable modules over this algebra is in bijection with the latt ice of Kauffman states. This bijection allows us to compute the Alexander polynomial of a knot with a specialization of the F-polynomial of any inde composable module over this algebra.\nAfter a brief introduction to knot t heory\, I will explain how to compute an Alexander polynomial from a F-pol ynomial.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/79 / END:VEVENT BEGIN:VEVENT SUMMARY:Gonçalo Tabuada (Warwick) DTSTART;VALUE=DATE-TIME:20220221T130000Z DTEND;VALUE=DATE-TIME:20220221T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/80 DESCRIPTION:Title: Jacques Tits motivic measure\nby Gonçalo Tabuad a (Warwick) as part of Paris algebra seminar\n\n\nAbstract\nThe Grothendie ck ring of varieties\, introduced in a letter from Alexander Grothendieck to Jean-Pierre Serre (August 16th 1964)\, plays an important role in algeb raic geometry. However\, despite the efforts of several mathematicians\, t he structure of this ring still remains poorly understood. In order to cap ture some of the flavor of Grothendieck’s ring of varieties\, a few moti vic measures have been built throughout the years. In this talk I will pre sent a new motivic measure\, called the Jacques Tits motivic measure\, and describe some of its numerous applications.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/80 / END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Guy Plamondon (Versailles) DTSTART;VALUE=DATE-TIME:20220228T130000Z DTEND;VALUE=DATE-TIME:20220228T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/81 DESCRIPTION:Title: Cluster algebras\, categorification\, and some confi guration spaces\nby Pierre-Guy Plamondon (Versailles) as part of Paris algebra seminar\n\n\nAbstract\nThe real part of the configuration space M _{0\,n} of n points on a projective line has a connected component which i s closely related to the associahedron. As an affine variety\, it is defi ned by explicit equations which are in close connection with exchange rela tions for cluster variables in type A. This has been generalized to all D ynkin types.\n\nIn this talk\, we will construct an affine variety associa ted to any representation-finite finite-dimensional algebra over an algebr aically closed field. The equations defining the variety will be obtained from the F-polynomials of indecomposable modules over the algebra. This generalizes previous results\, which can be recovered by applying our cons truction to Jacobian algebras in Dynkin types.\n\nThis talk is based on an ongoing project with Nima Arkani-Hamed\, Hadleigh Frost\, Giulio Salvator i and Hugh Thomas.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/81 / END:VEVENT BEGIN:VEVENT SUMMARY:Léa Bittmann (Edinburgh) DTSTART;VALUE=DATE-TIME:20220425T120000Z DTEND;VALUE=DATE-TIME:20220425T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/82 DESCRIPTION:Title: A Schur-Weyl duality between Double Affine Hecke Alg ebras and quantum groups\nby Léa Bittmann (Edinburgh) as part of Pari s algebra seminar\n\nLecture held in hybrid.\n\nAbstract\nSchur-Weyl duali ty is often used to relate type A Lie groups (or quantum groups) to symmet ric groups (or Hecke algebras). In this talk\, I will use ribbon calculus and skein modules to describe an instance of this Schur-Weyl duality betwe en representations of the type A quantum group at roots of unity and repre sentations of the Double Affine Hecke Algebra. This is based on joint work with A. Chandler\, A. Mellit and C. Novarini.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/82 / END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Bitoun (Calgary) DTSTART;VALUE=DATE-TIME:20220516T120000Z DTEND;VALUE=DATE-TIME:20220516T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/83 DESCRIPTION:Title: On centralizers in Azumaya domains\nby Thomas Bi toun (Calgary) as part of Paris algebra seminar\n\nLecture held in hybrid. \n\nAbstract\nWe prove a positive characteristic analogue of the classical result that the centralizer of a nonconstant differential operator in one variable is commutative. This leads to a new\, short proof of that classi cal characteristic zero result\, by reduction modulo p. This is joint work with Justin Desrochers available at https://arxiv.org/abs/2201.04606.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/83 / END:VEVENT BEGIN:VEVENT SUMMARY:Alex Takeda (IHES) DTSTART;VALUE=DATE-TIME:20220307T130000Z DTEND;VALUE=DATE-TIME:20220307T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/84 DESCRIPTION:Title: The ribbon quiver complex and the noncommutative Leg endre transform\nby Alex Takeda (IHES) as part of Paris algebra semina r\n\n\nAbstract\nThe structure of a fully extended oriented 2d TQFT is giv en by a Frobenius algebra. If one wants to lift this structure to a cohomo logical field theory\, the correct notion is that of a Calabi-Yau algebra or category\; the CohFT operations can be described by a certain graph com plex. There are two different notions of Calabi-Yau structure on categorie s\, both requiring some type of finiteness or dualizability. In this talk I will discuss a variation that works in non-dualizable cases as well\; in this case the graphs get replaced by quivers. The resulting complex calcu lates the homology of certain moduli spaces of open-closed surfaces\, and can be used to give a fully explicit description of these operations. In t he second half of the talk\, I will describe some of these constructions\, including how to produce operations from smooth and/or relative Calabi-Ya u structures\, and explain how\, in the smooth case\, this can be thought of as a noncommutative version of the Legendre transform. This is joint wo rk with M. Kontsevich and Y. Vlassopoulos.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/84 / END:VEVENT BEGIN:VEVENT SUMMARY:Norihiro Hanihara (Nagoya) DTSTART;VALUE=DATE-TIME:20220321T130000Z DTEND;VALUE=DATE-TIME:20220321T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/85 DESCRIPTION:Title: Tilting theory via enhancements\nby Norihiro Han ihara (Nagoya) as part of Paris algebra seminar\n\n\nAbstract\nTilting the ory aims at giving equivalences among various triangulated categories\, su ch as derived categories\, cluster categories\, and singularity categories . Constructing such an equivalence provides a mutual understanding of thes e categories. In this talk\, we study tilting theory for singularity categ ories and cluster categories from the viewpoint of dg enhancements. We wil l first review their construction in terms of their enhancements\, and the n based on this we explain a general method of giving equivalences between singularity categories and cluster categories. Our main steps are existen ce of (weak) right Calabi-Yau structure on the dg singularity category of commutative Gorenstein rings\, and a characterization of dg orbit categori es among bigraded dg categories. This is a joint work with Osamu Iyama.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/85 / END:VEVENT BEGIN:VEVENT SUMMARY:Jie Pan (Zhejiang U.) DTSTART;VALUE=DATE-TIME:20220314T130000Z DTEND;VALUE=DATE-TIME:20220314T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/86 DESCRIPTION:Title: Positivity and polytope basis in cluster algebras vi a Newton polytopes\nby Jie Pan (Zhejiang U.) as part of Paris algebra seminar\n\n\nAbstract\nWe work in the generality of a totally sign-skew-sy mmetric (e.g. skew-symmetrizable) \ncluster algebra of rank $n$. We study the Newton polytopes of $F$-polynomials and\, more generally\, a\nfamily o f polytopes $N_h$ indexed by vectors $h$ in $Z^n$. We use it to give a new proof of Laurent \npositivity and to construct what we call the polytope basis of the upper cluster algebra. The polytope \nbasis consists of certa in universally indecomposable Laurent polynomials. It is strongly positive \nand generalizes the greedy basis constructed by Lee-Li-Zelevinsky in ran k 2.\nThis is a report on joint work with Fang Li\, cf. arXiv:2201.01440.\ n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/86 / END:VEVENT BEGIN:VEVENT SUMMARY:Asilata Bapat (Australian National U.) DTSTART;VALUE=DATE-TIME:20220328T120000Z DTEND;VALUE=DATE-TIME:20220328T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/87 DESCRIPTION:Title: Categorical q-deformed rational numbers via Bridgela nd stability conditions\nby Asilata Bapat (Australian National U.) as part of Paris algebra seminar\n\n\nAbstract\nWe will discuss new categoric al interpretations of two distinct q-deformations of the rational numbers. The first one\, introduced by Morier-Genoud and Ovsienko in a different c ontext\, enjoys fascinating combinatorial\, topological\, and algebraic pr operties. The second one is a natural partner to the first\, and is new. W e obtain these deformations via boundary points of a compactification of t he space of Bridgeland stability conditions on the 2-Calabi-Yau category o f the A2 quiver. The talk is based on joint work with Louis Becker\, Anand Deopurkar\, and Anthony Licata.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/87 / END:VEVENT BEGIN:VEVENT SUMMARY:Hipolito Treffinger (City University of Paris) DTSTART;VALUE=DATE-TIME:20220404T120000Z DTEND;VALUE=DATE-TIME:20220404T123000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/88 DESCRIPTION:Title: Torsion classes and tau-tilting in higher homologica l algebra\, I\nby Hipolito Treffinger (City University of Paris) as pa rt of Paris algebra seminar\n\nLecture held in hybrid.\n\nAbstract\nHigher homological algebra was introduced by Iyama in the late \n2000's. His poi nt of view was that some classical results by Auslander \nand Auslander--R eiten were somehow 2-dimensional and should have \nn-dimensional equivalen ts. This new theory quickly attracted a lot of \nattention\, with many aut hors generalising classical notions to the \nsetting of higher homological algebra. Examples of such generalisations \nare the introduction of n-abe lian categories by Jasso\, n-angulated \ncategories by Geiss--Keller--Oppe rmann\, and n-torsion classes by Jørgensen.\n\nRecently\, it was shown by Kvamme and\, independently\, by Ebrahimi and \nNasr-Isfahani\, that every small n-abelian category is the \nn-cluster-tilting subcategory of an abe lian category. In this talk\, we \nwill focus on the relation between n-to rsion classes in an n-abelian \ncategory $\\mathcal{M}$ and (classical) to rsion classes of the abelian \ncategory $\\mathcal{A}$ in which $\\mathcal {M}$ is embedded. By \nconsidering functorially finite torsion classes\, t his will allow us to \nrelate n-torsion classes with maximal tau_n-rigid o bjects in $\\mathcal{M}$.\n\nSome of the results presented in this talk ar e part of a joint work by \nJ. Asadollahi\, P. Jørgensen\, S. Schroll\, H . Treffinger. The rest \ncorresponds to an ongoing project by J. August\, J. Haugland\, \nK. Jacobsen\, S. Kvamme\,Y. Palu and H. Treffinger.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/88 / END:VEVENT BEGIN:VEVENT SUMMARY:Yann Palu (Amiens) DTSTART;VALUE=DATE-TIME:20220404T123000Z DTEND;VALUE=DATE-TIME:20220404T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/89 DESCRIPTION:Title: Torsion classes and tau-tilting in higher homologica l algebra\, II\nby Yann Palu (Amiens) as part of Paris algebra seminar \n\nLecture held in hybrid.\n\nAbstract\nHigher homological algebra was in troduced by Iyama in the late \n2000's. His point of view was that some cl assical results by Auslander \nand Auslander--Reiten were somehow 2-dimens ional and should have \nn-dimensional equivalents. This new theory quickly attracted a lot of \nattention\, with many authors generalising classical notions to the \nsetting of higher homological algebra. Examples of such generalisations \nare the introduction of n-abelian categories by Jasso\, n-angulated \ncategories by Geiss--Keller--Oppermann\, and n-torsion class es by Jørgensen.\n\nRecently\, it was shown by Kvamme and\, independently \, by Ebrahimi and \nNasr-Isfahani\, that every small n-abelian category i s the \nn-cluster-tilting subcategory of an abelian category. In this talk \, we \nwill focus on the relation between n-torsion classes in an n-abeli an \ncategory $\\mathcal{M}$ and (classical) torsion classes of the abelia n \ncategory $\\mathcal{A}$ in which $\\mathcal{M}$ is embedded. By \ncons idering functorially finite torsion classes\, this will allow us to \nrela te n-torsion classes with maximal tau_n-rigid objects in $\\mathcal{M}$.\n \nSome of the results presented in this talk are part of a joint work by \ nJ. Asadollahi\, P. Jørgensen\, S. Schroll\, H. Treffinger. The rest \nco rresponds to an ongoing project by J. August\, J. Haugland\, \nK. Jacobsen \, S. Kvamme\,Y. Palu and H. Treffinger.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/89 / END:VEVENT BEGIN:VEVENT SUMMARY:Peigen Cao (Hebrew University) DTSTART;VALUE=DATE-TIME:20220411T120000Z DTEND;VALUE=DATE-TIME:20220411T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/90 DESCRIPTION:Title: On exchange matrices from string diagrams\nby Pe igen Cao (Hebrew University) as part of Paris algebra seminar\n\nLecture h eld in Zoom.\n\nAbstract\nIn this talk\, we will first recall the construc tions of triangular extension and of source-sink extensio for skew-symmetr izable matrices and some invariants under these constructions. Secondly\, we will recall the string diagrams introduced by Shen-Weng\, which are ver y useful to describe many interesting skew-symmetrizable matrices closely related with Lie theory. Thirdly\, we will sketch the proof of our main re sult: the skew-symmetrizable matrices from string diagrams are in the smal lest class of skew-symmetrizable matrices containing the (1 times 1) zero matrix and closed under mutations and source-sink extensions. This result applies to the exchange matrices of cluster algebras from double Bruhat ce lls\, unipotent cells\, double Bott-Samelson cells among others. Finally\, some immediate applications regarding reddening sequences and non-degener ate potentials for many quivers from Lie theory are given.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/90 / END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Vallette (Sorbonne Paris Nord) DTSTART;VALUE=DATE-TIME:20220523T120000Z DTEND;VALUE=DATE-TIME:20220523T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/91 DESCRIPTION:Title: Pre-Calabi-Yau algebras and homotopy double Poisson gebras\nby Bruno Vallette (Sorbonne Paris Nord) as part of Paris algeb ra seminar\n\n\nAbstract\nWe prove that the notion of a curved pre-Calabi –Yau algebra is equivalent to the notion of a curved homotopy double Poi sson gebra\, thereby settling the equivalence between the two ways to defi ne derived noncommutative Poisson structures. We actually prove that the r espective differential graded Lie algebras controlling both deformation th eories are isomorphic. This allows us to apply the recent developments of the properadic calculus in order to establish the homotopical properties o f curved pre-Calabi–Yau algebras: infini-morphisms\, homotopy transfer t heorem\, formality\, Koszul hierarchy\, and twisting procedure. (Joint wor k with Johan Leray available at arxiv.org/abs/2203.05062).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/91 / END:VEVENT BEGIN:VEVENT SUMMARY:Tasuki Kinjo (IPMU) DTSTART;VALUE=DATE-TIME:20220502T120000Z DTEND;VALUE=DATE-TIME:20220502T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/92 DESCRIPTION:Title: Deformed Calabi--Yau completion and its application to DT theory\nby Tasuki Kinjo (IPMU) as part of Paris algebra seminar\ n\n\nAbstract\nIn this talk\, we investigate an application of the theory of deformed Calabi--Yau completion to enumerative geometry. The notion of Calabi--Yau completion was first introduced by Keller as a non-commutative analogue of the canonical bundle. In the same paper\, he also introduced a deformed version of the Calabi--Yau completion.\nWe will explain that th e deformed Calabi--Yau completion is a non-commutative analogue of an affi ne bundle modeled on the canonical bundle. Combining this observation with a recent work of Bozec--Calaque--Scherotzke\, we prove that the moduli sp ace of coherent sheaves on a certain non-compact Calabi--Yau threefold is described as the critical locus inside a smooth moduli space. This descrip tion has several applications in Donaldson--Thomas theory including Toda's \\chi-independence conjecture of Gopakumar--Vafa invariants for arbitrary local curves. By dimensional reduction\, it implies (and extends) Hausel- -Thaddeus's cohomological \\chi-independence conjecture for Higgs bundles. \n\nThis talk is based on a joint work with Naruki Masuda and another join t work with Naoki Koseki.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/92 / END:VEVENT BEGIN:VEVENT SUMMARY:Florian Naef DTSTART;VALUE=DATE-TIME:20220509T120000Z DTEND;VALUE=DATE-TIME:20220509T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/93 DESCRIPTION:Title: The (non-)homotopy invariance of the string coproduc t\nby Florian Naef as part of Paris algebra seminar\n\n\nAbstract\nA C alabi-Yau structure on a smooth algebra allows one to identify Hochschild homology with Hochschild cohomology. With this identification Hochschild h omology acquires an additional Gerstenhaber algebra structure. One way to formulate the amount of structure one has on Hochschild homology is to enc ode it into a 2d TFT. This explains some of the string topology operations on the free loop space of a manifold\, but not the string coproduct. If t he algebra has additional structure (trivialization of its Hattori-Stallin g Euler characteristic) one obtains an extra secondary operation on Hochsc hild homology\, which recovers the string coproduct. Finally\, in the free loop space setting\, this additional structure can either be recovered fr om intersection theory of the manifold or from its underlying simple homot opy type\, thus relating the two. Using this last relation one can express the difference between the string coproduct of two homotopic but not nece ssarily homeomorphic manifolds in terms of Whitehead torsion.\nThis is joi nt work with Pavel Safronov\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/93 / END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Rickard (Bristol) DTSTART;VALUE=DATE-TIME:20220606T120000Z DTEND;VALUE=DATE-TIME:20220606T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/94 DESCRIPTION:Title: Generating the derived category\nby Jeremy Ricka rd (Bristol) as part of Paris algebra seminar\n\n\nAbstract\nThe unbounded derived category of (right) modules over a ring is a triangulated categor y with infinite products and coproducts. As a triangulated category with c oproducts it is easy to see that it is generated by the projective modules \, and similarly it is generated as a triangulated category with products by the injective modules.\n\nI will discuss the question of whether it is generated as a triangulated category with coproducts by the injective modu les\, or as a triangulated category with products by the projective (or fl at) modules. I will describe the relationship with the finitistic dimensio n conjecture\, as well as some more recent results.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/94 / END:VEVENT BEGIN:VEVENT SUMMARY:Yuya Mizuno (Osaka Metropolitan University) DTSTART;VALUE=DATE-TIME:20220613T120000Z DTEND;VALUE=DATE-TIME:20220613T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/95 DESCRIPTION:Title: g-simplicial complex and silting theory\nby Yuya Mizuno (Osaka Metropolitan University) as part of Paris algebra seminar\n \n\nAbstract\nFor a finite dimensional algebra $A$\, the 2-term silting co mplexes of $A$ give a simplicial complex $\\Delta(A)$\, which is called th e g-simplicial complex.\nWe study several properties of $\\Delta(A)$ and\, in particular\, we give tilting theoretic interpretations of the $h$-vect ors and the Dehn-Sommerville equations of $\\Delta(A)$.\nConsequently\, w e can explain a close correspondence between torsion classes and wide subc ategories\, which can be regarded as a refinement of the Koenig-Yang corre spondence.\nThis is joint work with Aoki-Higashitani-Iyama-Kase\, cf. http s://arxiv.org/pdf/2203.15213.pdf\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/95 / END:VEVENT BEGIN:VEVENT SUMMARY:Jens Niklas Eberhardt (Bonn) DTSTART;VALUE=DATE-TIME:20220530T120000Z DTEND;VALUE=DATE-TIME:20220530T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/96 DESCRIPTION:Title: Motivic Springer Theory\nby Jens Niklas Eberhard t (Bonn) as part of Paris algebra seminar\n\n\nAbstract\nAlgebras and thei r representations can often be constructed geometrically in terms of convo lution of cycles. \nFor example\, the Springer correspondence describes ho w irreducible representations of a Weyl group can be realised in terms of a convolution action on the vector spaces of irreducible components of Spr inger fibers. Similar situations yield the affine Hecke algebra\, quiver H ecke algebra (KLR algebra)\, quiver Schur algebra or Soergel bimodules.\nI n this spirit\, we show that these algebras and their representations can be realised in terms of certain equivariant motivic sheaves called Springe r motives.\nOn our way\, we will discuss weight structures and their appli cations to motives.\nThis is joint work with Catharina Stroppel.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/96 / END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Shapiro (Edinburgh) DTSTART;VALUE=DATE-TIME:20220620T120000Z DTEND;VALUE=DATE-TIME:20220620T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/97 DESCRIPTION:Title: Positive representation theory\nby Alexander Sha piro (Edinburgh) as part of Paris algebra seminar\n\n\nAbstract\nThe notio ns of a modular tensor category\, 2d topological modular functor\, and 3d topological quantum field theory are essentially equivalent. Fock and Gonc harov conjectured that the quantised higher Teichmüller theory gives rise to an analogue of a modular functor. Their construction in turn yields a family of "positive" representations of quantum groups. I will argue that these representations provide a compelling first step towards constructing an analogue of a modular tensor category. This talk will be based on join t works with Gus Schrader.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/97 / END:VEVENT BEGIN:VEVENT SUMMARY:Daping Weng (UC Davis) DTSTART;VALUE=DATE-TIME:20220627T120000Z DTEND;VALUE=DATE-TIME:20220627T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/98 DESCRIPTION:Title: Grid plabic graphs\, Legendrian weaves\, and (quasi- )cluster structures\nby Daping Weng (UC Davis) as part of Paris algebr a seminar\n\n\nAbstract\nGiven a plabic graph on R^2\, we can choose a con ormal lift of its zig-zag strands to the unit cotangent bundle of R^2\, ob taining a Legendrian link. If the plabic graph satisfies a “grid” cond ition\, its Legendrian link admits a natural embedding into the standard c ontact R^3. We study the Kashiwara-Schapira moduli space of microlocal ran k 1 sheaves associated with the Legendrian link\, and construct a natural (quasi-)cluster structure on this moduli space using Legendrian weaves. In particular\, we prove that any braid variety associated with (beta Delta) for a 3-strand braid beta admits cluster structures with an explicit cons truction of initial seeds. We also construct Donaldson-Thomas transformati ons for these moduli spaces and prove that the upper cluster algebra equal s its cluster algebra. In this talk\, I will introduce the theoretical bac kground and describe the basic combinatorics for constructing Legendrian w eaves and the (quasi-)cluster structures from a grid plabic graph. This is based on joint work with Roger Casals\, cf. https://arxiv.org/abs/2204.13 244.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/98 / END:VEVENT BEGIN:VEVENT SUMMARY:Sibylle Schroll (Cologne) DTSTART;VALUE=DATE-TIME:20220704T120000Z DTEND;VALUE=DATE-TIME:20220704T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/99 DESCRIPTION:Title: Recollements of derived categories of graded gentle algebras\nby Sibylle Schroll (Cologne) as part of Paris algebra semina r\n\n\nAbstract\nGraded gentle algebras are classical objects in represent ation theory. They are quadratic monomial algebras making them particularl y amenable to study and they appear in many different areas of mathematics such as in cluster theory\, in N=2 gauge theories and in homological mirr or symmetry of surfaces. \nIn this talk\, we give a construction of a part ial cofibrant dg algebra resolution of a graded quadratic monomial algebra inducing an explicit recollement of their derived categories. We show tha t for graded gentle algebras\, both the left and the right side of such a recollement corresponds to cutting the underlying surface which can be ass ociated to a graded gentle algebra. In the case of homologically smooth an d proper graded gentle algebras this recollement can be restricted to the derived categories with finite total cohomology\, thus inducing a recollem ent of the corresponding partially wrapped Fukaya categories. We give some consequences of this construction such as the existence of full exception al sequences\, silting objects and simple minded collections. This is join t work with Wen Chang and Haibo Jin https://arxiv.org/abs/2206.11196.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/99 / END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Labardini-Fragoso (UNAM) DTSTART;VALUE=DATE-TIME:20221107T130000Z DTEND;VALUE=DATE-TIME:20221107T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/100 DESCRIPTION:Title: Revisiting Derksen-Weyman-Zelevinsky's mutations\nby Daniel Labardini-Fragoso (UNAM) as part of Paris algebra seminar\n\n Lecture held in room 01 of the Institut Henri Poincaré\, Paris\, France.\ n\nAbstract\nThe mutation theory of quivers with potential and their repre sentations\, developed around 15 years ago by Derksen-Weyman-Zelevinsky\, has had a profound impact both inside and outside the theory of cluster al gebras. In this talk I will present results obtained in joint works with G eiss and Schröer\, and with de Laporte\, about some interesting behaviors of DWZ's mutations of representations. Namely\, despite needing several n on-canonical choices of linear-algebraic data in order to be performed\, t hey can always be arranged so as to become regular maps on dense open subs ets of representation spaces rep(Q\,S\,d). As a consequence\, one obtains the invariance of Geiss-Leclerc-Schröer's 'generic basis' under mutations even in the Jacobi-infinite case\, thus generalizing a result of Plamondo n. Furthermore\, given two distinct vertices k\, \\ell of a quiver with po tential (Q\,S)\, the k-th mutation of representations takes the \\ell-th i ndecomposable projective over (Q\,S) to the \\ell-th indecomposable projec tive over \\mu_k(Q\,S). When a certain 'optimization' condition is satisfi ed by \\ell\, this allows to compute certain 'Landau-Ginzburg potentials' as F-polynomials of projective representations.\n\nIn-person talk at the r oom 01 of the Institut Henri Poincaré\, Paris\, France\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Greg Muller (Oklahoma) DTSTART;VALUE=DATE-TIME:20221010T120000Z DTEND;VALUE=DATE-TIME:20221010T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/101 DESCRIPTION:Title: Juggler's friezes\nby Greg Muller (Oklahoma) as part of Paris algebra seminar\n\n\nAbstract\nFrieze patterns are infinite strips of numbers satisfying certain determinantal identities. Originally motivated by Gauss’ “miraculous pentagram” identities\, these patte rns have since been connected to triangulations\, integrable systems\, rep resentation theory\, and cluster algebras. In this talk\, we will review a few characterizations and constructions of frieze patterns\, as well as a generalization which allows friezes with a “ragged edge” described by a juggling function. These “juggler’s friezes” correspond to specia l points in positroid varieties\, in direct analogy with how classical fri ezes correspond to special points in Grassmannians.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Linhui Shen (Michigan State) DTSTART;VALUE=DATE-TIME:20221017T120000Z DTEND;VALUE=DATE-TIME:20221017T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/102 DESCRIPTION:Title: Cluster Nature of Quantum Groups\nby Linhui She n (Michigan State) as part of Paris algebra seminar\n\n\nAbstract\nWe pres ent a rigid cluster model to realize the quantum group $U_q(g)$ for $g$ of type ADE. That is\, we prove that there is a natural Hopf algebra isomorp hism from the quantum group to a quotient algebra of the Weyl group invari ants of a Fock-Goncharov quantum cluster algebra. By applying the quantum duality of cluster algebras\, we show that the quantum group admits a clus ter canonical basis $\\Theta$ whose structural coefficients are in $\\math bb{N}[q^{\\frac{1}{2}}\, q^{-\\frac{1}{2}}]$. The basis $\\Theta$ satisfie s an invariance property under Lusztig's braid group action\, the Dynkin a utomorphisms\, and the star anti-involution.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Slava Pimenov (Nottingham) DTSTART;VALUE=DATE-TIME:20221003T120000Z DTEND;VALUE=DATE-TIME:20221003T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/103 DESCRIPTION:Title: Planar Prop of Differential Operators of Associativ e Algebras\nby Slava Pimenov (Nottingham) as part of Paris algebra sem inar\n\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleven speakers DTSTART;VALUE=DATE-TIME:20220905T120000Z DTEND;VALUE=DATE-TIME:20220905T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/104 DESCRIPTION:Title: Algebra days in Paris\nby Eleven speakers as pa rt of Paris algebra seminar\n\n\nAbstract\nYou may be interested in the el even talks delivered on September 5 and 6 at the Algebra days in Paris.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Kapranov (Yale and IPMU) DTSTART;VALUE=DATE-TIME:20220912T120000Z DTEND;VALUE=DATE-TIME:20220912T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/105 DESCRIPTION:Title: Perverse sheaves and schobers on symmetric products \nby Mikhail Kapranov (Yale and IPMU) as part of Paris algebra seminar \n\n\nAbstract\nThe talk\, based on joint work in progress with V. Schecht man\, will first recall our description of perverse sheaves on $Sym^n(\\ma thbb{C})$\, the symmetric product of the complex line with its natural str atification by multiplicities. This description proceeds in terms of conti ngency matrices\, which are certain integer matrices appearing (besides th eir origin in statistics) in three different contexts:\n\n- A natural cell decomposition of $Sym^n(\\mathbb{C})$.\n\n- Compatibility of multiplicati on and comultiplication in $\\mathbb{Z}_+$-graded Hopf algebras.\n\n- Para bolic Bruhat decomposition for $GL_n$.\n\nPerverse sheaves on $Sym^n(\\mat hbb{C})$ are described in terms of certain data of mixed functoriality on contingency matrices which we call Janus sheaves. I will then explain our approach to categorifying the concept of Janus sheaves\, in which sums are replaced by filtrations with respect to the Bruhat order. Such data can b e called Janus schobers. Examples can be obtained from $\\mathbb{Z}_+$-gra ded Hopf categories\, a concept going back to Crane-Frenkel\, of which we consider two examples related to representations of groups $GL_n$ over fin ite fields (Joyal-Street) and $p$-adic fields (Bernstein-Zelevinsky). [Thi s talk is kindly shared by Noncommutativ e shapes.]\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Amnon Neeman (Australian National University) DTSTART;VALUE=DATE-TIME:20220926T120000Z DTEND;VALUE=DATE-TIME:20220926T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/106 DESCRIPTION:Title: Two results\, both developments of a 2015 article b y Krause\nby Amnon Neeman (Australian National University) as part of Paris algebra seminar\n\n\nAbstract\nIn 2020\, the pandemic hit\, and all around the globe we went into lockdowns of various description. During the first lockdown I carefully read Krause's 2015 article "Deriving Auslander 's formula".\n\nIn this talk\, I will outline how the ideas of Krause's pa per underpin two articles written in 2020 in collaboration with Canonaco a nd Stellari. One is about the uniqueness of enhancements of large classes of triangulated categories\, while the second offers a counterexample to c ertain vanishing conjectures in negative K-theory. [This talk is kindly sh ared by Representation theory and triangulated categories.]\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 6/ END:VEVENT BEGIN:VEVENT SUMMARY:Liran Shaul (Prague) DTSTART;VALUE=DATE-TIME:20220919T120000Z DTEND;VALUE=DATE-TIME:20220919T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/107 DESCRIPTION:Title: The finitistic dimension conjecture via DG-rings\nby Liran Shaul (Prague) as part of Paris algebra seminar\n\n\nAbstract\ nThe finitistic dimension of a ring A is defined to be the supremum of pro jective dimensions among all A-modules of finite projective dimension. It is an open problem whether this quantity is finite for finite dimensional algebras over a field and for artin algebras.\n\nIn this talk\, I will exp lain a new approach for studying the finiteness of the finitistic dimensio n by embedding the ring A inside a nicely behaved differential graded alge bra\, and using relation between this DG-algebra and A to deduce results a bout the finitistic dimension.\nAs an application of these methods\, I wil l explain how to generalize a recent sufficient condition of Rickard\, for FPD(A)<∞ in terms of generation of D(A) from finite dimensional algebra s over a field to all left perfect rings which admit a dualizing complex.\ n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Sauter (Bielefeld) DTSTART;VALUE=DATE-TIME:20221024T120000Z DTEND;VALUE=DATE-TIME:20221024T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/108 DESCRIPTION:Title: Tilting theory in exact categories\nby Julia Sa uter (Bielefeld) as part of Paris algebra seminar\n\n\nAbstract\nWe define tilting subcategories in arbitrary exact categories to archieve the follo wing. Firstly: Unify existing definitions of tilting subcategories to arbi trary exact categories. Discuss standard results for tilting subcategories : Auslander correspondence\, Bazzoni description of the perpendicular cate gory. Secondly: We treat the question of induced derived equivalences sepa rately - given a tilting subcategory T\, we ask if a functor on the perpen dicular category induces a derived equivalence to a (certain) functor cate gory over T. If this is the case\, we call the tilting subcategory ideq ti lting. We prove a generalization of Miyashita's theorem (which is itself a generalization of a well-known theorem of Brenner-Butler) and characteriz e exact categories with enough projectives allowing ideq tilting subcatego ries. In particular\, this is always fulfilled if the exact category is ab elian with enough projectives.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Sota Asai (Osaka) DTSTART;VALUE=DATE-TIME:20221031T130000Z DTEND;VALUE=DATE-TIME:20221031T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/109 DESCRIPTION:Title: TF equivalence classes and canonical decompositions for E-tame algebras\nby Sota Asai (Osaka) as part of Paris algebra se minar\n\n\nAbstract\nThis is joint work with Osamu Iyama. Let $A$ be a fin ite dimensional algebra over an algebraically closed field. Then the numer ical torsion pairs of Baumann-Kamnitzer-Tingley give an equivalence relati on on the real Grothendieck group of finitely generated projective $A$-mod ules\, which is called TF equivalence. By results of Yurikusa and Bruestle -Smith-Treffinger\, we have that the g-vector cone of each 2-term presilti ng complex is a TF equivalence class. To get more TF equivalence classes\, we can use canonical decompositions of elements in the (integral) Grothen dieck group of finitely generated projectives introduced by Derksen-Fei. W e have showed that the cone defined by the canonical decomposition of each element is contained in some single TF equivalence class. Moreover\, we h ave also obtained that\, if $A$ is an E-tame algebra\, then this cone is p recisely a TF equivalence class. In this talk\, I will explain these resul ts and some important steps to prove them.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/10 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Marin (Amiens and CNRS) DTSTART;VALUE=DATE-TIME:20221114T130000Z DTEND;VALUE=DATE-TIME:20221114T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/110 DESCRIPTION:Title: Geometric realization via random variables\nby Ivan Marin (Amiens and CNRS) as part of Paris algebra seminar\n\nLecture h eld in room 01 of the Institut Henri Poincaré\, Paris\, France.\n\nAbstra ct\nTopological spaces up to (weak) equivalences are\nfaithfully represent ed by simplicial combinatorial\nstructures. Through an identification of t he\n$n$-dimensional simplex with the space of probability\nmeasures on a f inite set of size $n+1$\, we investigate\nwhat happens when it is replaced by the\nspace of random variables that naturally lies 'above' it.\nBy thi s procedure\, we obtain in particular a simple description\nof the classif ying set of a (discrete) group\, and also\na new concept of geometric real ization. This new one\nalso induces an equivalence of categories up to hom otopy\nwith simplicial sets and topological spaces. The 'probability-law'\ nmap then defines a natural transformation between the\ntwo corresponding Quillen equivalences.\n\nIn-person talk at the room 01 of the Institut Hen ri Poincaré\, Paris\, France\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Euiyong Park (Seoul) DTSTART;VALUE=DATE-TIME:20221205T130000Z DTEND;VALUE=DATE-TIME:20221205T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/111 DESCRIPTION:Title: Extended crystal structures of Hernandez-Leclerc ca tegories\nby Euiyong Park (Seoul) as part of Paris algebra seminar\n\n \nAbstract\nIn this talk\, we will discuss the categorical crystal structu re on the Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$. We de fine extended crystals for quantum groups and show that there is a braid g roup action on extended crystals. We then explain how the set of the isom orphism classes of simple modules in $\\mathscr{C}_\\mathfrak{g}^0$ has an extended crystal structure\, and discuss the braid group action from the viewpoint of the Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$ . This talk is based on joint work with M. Kashiwara (arXiv: 2111.07255 an d 2207.11644).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Gustavo Jasso and Fernando Muro (Lund and Sevilla) DTSTART;VALUE=DATE-TIME:20221121T130000Z DTEND;VALUE=DATE-TIME:20221121T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/112 DESCRIPTION:Title: The triangulated Auslander-Iyama correspondence\, I \nby Gustavo Jasso and Fernando Muro (Lund and Sevilla) as part of Par is algebra seminar\n\n\nAbstract\nIn these two talks\, we will start by in troducing a result which establishes the existence and uniqueness of (DG) enhancements for triangulated categories which admit an additive generator whose endomorphism algebra is finite-dimensional (over a perfect field). We will then present a generalisation of this result that allows us to tre at a larger class of triangulated categories\, which instead admit a gener ator with a strong regularity property (a so-called dZ-cluster tilting obj ect). We will also explain how our result\, combined with crucial theorems of August and Hua-Keller\, leads to a positive solution of the Donovan-We myss Conjecture for contraction algebras as observed by Keller. We will al so comment on some details about the proof.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Muro and Gustavo Jasso (Sevilla and Lund) DTSTART;VALUE=DATE-TIME:20221128T130000Z DTEND;VALUE=DATE-TIME:20221128T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/113 DESCRIPTION:Title: The triangulated Auslander-Iyama correspondence\, I I\nby Fernando Muro and Gustavo Jasso (Sevilla and Lund) as part of Pa ris algebra seminar\n\n\nAbstract\nIn these two talks\, we will start by i ntroducing a result which establishes the existence and uniqueness of (DG) enhancements for triangulated categories which admit an additive generato r whose endomorphism algebra is finite-dimensional (over a perfect field). We will then present a generalisation of this result that allows us to tr eat a larger class of triangulated categories\, which instead admit a gene rator with a strong regularity property (a so-called dZ-cluster tilting ob ject). We will also explain how our result\, combined with crucial theorem s of August and Hua-Keller\, leads to a positive solution of the Donovan-W emyss Conjecture for contraction algebras as observed by Keller. We will a lso comment on some details about the proof.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaël Rouquier (UCLA) DTSTART;VALUE=DATE-TIME:20221212T130000Z DTEND;VALUE=DATE-TIME:20221212T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/114 DESCRIPTION:Title: Coherent realizations of 2-representations\nby Raphaël Rouquier (UCLA) as part of Paris algebra seminar\n\n\nAbstract\n2 -representations of Kac-Moody algebras arise algebraically and as categori es of constructible sheaves. We will discuss two settings involving cohere nt sheaves: derived cotangent bundles to spaces of quiver representations and spaces of quasi-maps in flag varieties.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Alireza Nasr-Isfahani (IPM Isfahan) DTSTART;VALUE=DATE-TIME:20230116T130000Z DTEND;VALUE=DATE-TIME:20230116T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/115 DESCRIPTION:Title: Lower bound cluster algebras generated by projectiv e cluster variables\nby Alireza Nasr-Isfahani (IPM Isfahan) as part of Paris algebra seminar\n\n\nAbstract\nWe introduce the notion of a lower ( upper) bound cluster algebra generated by projective cluster variables. Pr ojective cluster variables are often categorified\nby projective modules o f the corresponding quiver with relations.\nWe show that under an acyclici ty assumption\, the cluster algebra and the lower bound cluster\nalgebra g enerated by projective cluster variables coincide.\nIn this case\, we use our results to construct a basis for the cluster algebra.\nWe also show th at the coincidence between cluster algebra and the lower bound cluster\nal gebra generated by projective cluster variables holds beyond acyclic seeds . Part of this talk is based on joint work with Karin Baur. - This talk wi ll be on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Duc-Khanh Nguyen (University at Albany) DTSTART;VALUE=DATE-TIME:20230123T130000Z DTEND;VALUE=DATE-TIME:20230123T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/116 DESCRIPTION:Title: A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schur and $k$-Schur functions\nby Duc-Khanh Nguyen (Universit y at Albany) as part of Paris algebra seminar\n\n\nAbstract\nWe introduce a generalization of $K$-$k$-Schur functions and k-Schur functions via the Pieri rule. Then we obtain the Murnaghan-Nakayama rule for the generalized functions. The rule is described explicitly in the cases of $K$-$k$-Schur functions and $k$-Schur functions\, with concrete descriptions and algori thms for coefficients. Our work recovers the result of Bandlow\, Schilling \, and Zabrocki for $k$-Schur functions\, and explains it as a degeneratio n of the rule for $K$-$k$-Schur functions. In particular\, many other spec ial cases promise to be detailed in the future. - This talk will be on Zoo m only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 6/ END:VEVENT BEGIN:VEVENT SUMMARY:Lauren Williams (Harvard) DTSTART;VALUE=DATE-TIME:20230605T120000Z DTEND;VALUE=DATE-TIME:20230605T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/117 DESCRIPTION:Title: The amplituhedron and cluster algebras\nby Laur en Williams (Harvard) as part of Paris algebra seminar\n\n\nAbstract\nI wi ll give a gentle introduction to the amplituhedron\, a geometric object th at was introduced in the context of scattering amplitudes in N=4 super Yan g Mills. I'll then explain some of the connections of the amplituhedron t o cluster algebras.\n\nThis talk will take place in hybrid mode at the Ins titut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Edmund Heng (IHES) DTSTART;VALUE=DATE-TIME:20230130T130000Z DTEND;VALUE=DATE-TIME:20230130T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/118 DESCRIPTION:Title: Coxeter quiver representations in fusion categories and Gabriel’s theorem\nby Edmund Heng (IHES) as part of Paris algeb ra seminar\n\n\nAbstract\nOne of the most celebrated theorems in the theor y of quiver representations is undoubtedly Gabriel’s theorem\, which rev eals a deep connection between quiver representations and root systems ari sing from Lie algebras. In particular\, Gabriel’s theorem shows that the finite-type quivers are classified by the ADE Dynkin diagrams and the ind ecomposable representations are in bijection with the underlying positive roots. Following the works of Dlab—Ringel\, the classification can be ge neralised to include all the other Dynkin diagrams (including BCFG) if one considers the more general notion of valued quivers (K-species) represent ations instead.\n\nWhile the theories above relate (valued) quiver represe ntations to root systems arising from Lie algebras\, the aim of this talk is to generalise Gabriel’s theorem in a slightly different direction usi ng root systems arising in Coxeter theory. Namely\, we shall introduce a n ew notion of Coxeter quivers and their representations built in (other) fu sion categories\, where we have a generalised Gabriel’s theorem as follo ws: a Coxeter quiver has finitely many indecomposable representations if a nd only if its underlying graph is a Coxeter-Dynkin diagram — including the non-crystallographic types H and I. Using a similar notion of reflecti on functors as introduced by Bernstein—Gelfand—Ponomarev\, we shall al so show that the isomorphism classes of indecomposable representations of a Coxeter quiver are in bijection with the positive roots associated to th e root system of the underlying Coxeter graph. --\nThis talk will take pla ce in hybrid mode at the IHP.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Fan Qin (Shanghai Jiao Tong) DTSTART;VALUE=DATE-TIME:20230220T130000Z DTEND;VALUE=DATE-TIME:20230220T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/119 DESCRIPTION:Title: Bracelets are theta functions for surface cluster a lgebras\nby Fan Qin (Shanghai Jiao Tong) as part of Paris algebra semi nar\n\n\nAbstract\nThe skein algebra of a marked surface admits the basis of bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-W illiams. As a cluster algebra\, it also admits the theta basis from the cl uster scattering diagram by Gross-Hacking-Keel-Kontsevich. In a joint work with Travis Mandel\, we show that the two bases coincide except for the o nce-punctured torus. Our results extend to quantum cluster algebras with c oefficients arising from the surface even in punctured cases. Long-standin g conjectures on strong positivity and atomicity follow as corollaries.\n\ nExceptionally\, this talk will take place in hybrid mode in room 1013 of the Sophie Germain building (8\, place Aurélie Nemours\, 75013 Paris).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/11 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Wille Liu (Taipei) DTSTART;VALUE=DATE-TIME:20230213T130000Z DTEND;VALUE=DATE-TIME:20230213T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/120 DESCRIPTION:Title: Translation functors for trigonometric double affin e Hecke algebras\nby Wille Liu (Taipei) as part of Paris algebra semin ar\n\n\nAbstract\nThe double affine Hecke algebra was introduced by Chered nik around 1995 as a tool in his study of Macdonald polynomials. Its degen erate version\, called trigonometric double affine Hecke algebra (TDAHA)\, has also turned out to be linked to different areas\, notably to the repr esentation theory of $p$-adic groups.\n\nGiven a root system\, the TDAHA $ H_c$ depends on a family of complex parameters $c$. Given two families of parameters $c$ and $c'$ whose difference takes integer values\, there exis ts a triangle equivalence between the bounded derived categories of the co rresponding TDAHAs\, which we call translation functor. The objective of t his talk is to explain the construction of this functor. \n\nThis talk wil l be on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Haruhisa Enomoto (Osaka Metropolitan) DTSTART;VALUE=DATE-TIME:20230227T130000Z DTEND;VALUE=DATE-TIME:20230227T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/121 DESCRIPTION:Title: Maximal self-orthogonal modules and a new generaliz ation of tilting modules\nby Haruhisa Enomoto (Osaka Metropolitan) as part of Paris algebra seminar\n\n\nAbstract\nWe study self-orthogonal modu les\, i.e.\, modules T such that Ext^i(T\, T) = 0 for all i > 0. We introd uce projectively Wakamatsu-tilting modules (pW-tilting modules) as a gener alization of tilting modules. If A is a representation-finite algebra\, ev ery self-orthogonal A-module can be completed to a pW-tilting module\, and the following classes coincide: pW-tilting modules\, Wakamatsu tilting mo dules\, maximal self-orthogonal modules\, and self-orthogonal modules T wi th |T| = |A|. We also prove that every self-orthogonal module over a repre sentation-finite Iwanaga-Gorenstein algebra has finite projective dimensio n. We finally explain some open conjectures on self-orthogonal modules.\n\ nThis talk will be on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Keyu Wang (Paris Cité) DTSTART;VALUE=DATE-TIME:20230206T130000Z DTEND;VALUE=DATE-TIME:20230206T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/122 DESCRIPTION:Title: QQ˜ -systems for twisted quantum affine algebras\nby Keyu Wang (Paris Cité) as part of Paris algebra seminar\n\n\nAbstr act\nAs a part of Langlands duality\, certain equations were found in two different areas of mathematics. They are known as Baxter’s TQ systems an d the QQ type systems\, as they trace back to Baxter’s study on integrab le models in the 1970s. During the same decade\, similar systems of equati ons were discovered in the area of ordinary differential equations (ODE) b y Sibuya\, Voros and others. Today\, this remarkable correspondence is rea lized as a duality between representation theory of nontwisted quantum aff ine algebras (QAA) and the theory of opers for their Langlands dual Lie al gebras.\n\nWe are interested in this duality when the roles of the affine Lie algebra and its dual are exchanged. When the nontwisted QAA is of type BCFG\, its dual will be a twisted QAA. To exchange their roles amounts to studying representations of twisted QAAs.\n\nIn this talk\, we will begin by reviewing this story. We will explain the representation theory of twi sted QAAs and their Borel algebras. We will explain the expected relations hip between twisted and nontwisted types\, and we will establish TQ system s and QQ^{~} systems for twisted QAAs.\n\nThis talk will take place in hyb rid mode at the IHP.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Amnon Yekutieli (Ben Gurion University) DTSTART;VALUE=DATE-TIME:20230403T120000Z DTEND;VALUE=DATE-TIME:20230403T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/123 DESCRIPTION:Title: An Algebraic Approach to the Cotangent Complex\ nby Amnon Yekutieli (Ben Gurion University) as part of Paris algebra semin ar\n\n\nAbstract\nLet $B/A$ be a pair of commutative rings. We propose an algebraic approach to the cotangent complex $L_{B/A}$. Using commutative s emi-free DG ring resolutions of B relative to A\, we construct a complex o f $B$-modules $LCot_{B/A}$. This construction works more generally for a p air $B/A$ of commutative DG rings.\n\nIn the talk\, we will explain all th ese concepts. Then we will discuss the important properties of the DG $B$- module $LCot_{B/A}$. It time permits\, we'll outline some of the proofs.\n \nIt is conjectured that for a pair of rings $B/A$\, our $LCot_{B/A}$ coin cides with the usual cotangent complex $L_{B/A}$\, which is constructed by simplicial methods. We shall also relate $LCot_{B/A}$ to modern homotopic al versions of the cotangent complex.\n\n\nSlides: https://sites.google.co m/view/amyekut-math/home/lectures/cotangent\n\n(updated 18 March 2023)\n\n \nThis talk will be on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Luc Pirio (Versailles) DTSTART;VALUE=DATE-TIME:20230306T130000Z DTEND;VALUE=DATE-TIME:20230306T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/124 DESCRIPTION:Title: Hyperlogarithmic functional identities on del Pezzo surfaces\nby Luc Pirio (Versailles) as part of Paris algebra seminar\ n\n\nAbstract\nFor any d in {1\,…\,6}\, we prove that the web of conics on a del Pezzo surface of degree d carries a functional identity HLog(7-d) whose components are antisymmetric hyperlogarithms of weight 7-d. Our app roach is uniform with respect to d and relies on classical results about t he action of the Weyl group on the set of lines on the del Pezzo surface. These hyperlogarithmic functional identities HLog(7-d) are natural genera lizations of the classical 3-term and (Abel's) 5-term identities of the l ogarithm and the dilogarithm\, which are the identities HLog(1) and HLog(2 ) corresponding to the cases d=6 and d=5 respectively.\n\nIf time allows\, I will give a list of many nice properties enjoyed by the 5-term identity of the dilogarithm and will explain that most of these properties (such a s being of cluster type) have natural generalizations which are satisfied by the weight 3 hyperlogarithmic identity HLog(3).\n\nThe talk will be mai nly based on the preprint arXiv:2301.06775 written with Ana-Maria Castrave t.\n\nExceptionally\, this talk will take place in hybrid mode in room 101 3 of the Sophie Germain building (8\, place Aurélie Nemours\, 75013 Paris ).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Julian Holstein (Hamburg) DTSTART;VALUE=DATE-TIME:20230313T130000Z DTEND;VALUE=DATE-TIME:20230313T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/125 DESCRIPTION:Title: Enriched Koszul duality for dg categories\nby J ulian Holstein (Hamburg) as part of Paris algebra seminar\n\n\nAbstract\nT he category of dg categories is related by Koszul duality to a certain cat egory of colagebras\, so-called pointed curved coalgebras. In this talk we wil review this Quillen equivalence and observe that it is in fact quasi- monoidal. By constructing internal homs of pointed curved coalgebras we ca n then construct a concrete closed monoidal model for dg categories. In pa rticular this gives natural descriptions of mapping spaces and internal ho ms between dg categories. This is joint work with A. Lazarev.\n\nException ally\, this talk will take place in hybrid mode in room 1013 of the Sophie Germain building (8\, place Aurélie Nemours\, 75013 Paris).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Reineke (Bochum) DTSTART;VALUE=DATE-TIME:20230320T130000Z DTEND;VALUE=DATE-TIME:20230320T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/126 DESCRIPTION:Title: Expander representations\nby Markus Reineke (Bo chum) as part of Paris algebra seminar\n\n\nAbstract\nDimension expanders\ , introduced by Wigderson and Lubotzky-Zelmanov\, are a linear algebra ana logue of the notion of expander graphs. We interpret this notion in terms of quiver representations\, as a quantitative variant of stability. We use Schofield’s recursive description of general subrepresentations to re-d erive existence of dimension expanders and to determine optimal expansion coefficients.\n\nThe talk will take place in hybrid mode at the IHP.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 6/ END:VEVENT BEGIN:VEVENT SUMMARY:Gleb Koshevoy (IHES) DTSTART;VALUE=DATE-TIME:20230327T120000Z DTEND;VALUE=DATE-TIME:20230327T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/127 DESCRIPTION:Title: Polyhedral parametrization of canonical bases\n by Gleb Koshevoy (IHES) as part of Paris algebra seminar\n\n\nAbstract\nPa rametrizations of the canonical bases\, string basis and theta basis\, ca n be obtained by the tropicalization of the Berenstein-Kazhdan decoration function and the Gross-Hacking-Keel-Kontsevich potential respectively. Fo r a classical Lie algebra and a reduced decomposition $\\mathbf i$\, the decorated graphs are constructed algorithmically\, vertices of such graph s are labeled by monomials which constitute the set of monomials of the Be renstein-Kazhdan potential. Due to this algorithm we obtain a characteri zation of $\\mathbf i$-trails introduced by Berenstein and Zelevinsky. Our algorithm uses multiplication and summations only\, its complexity is li near in time of writing the monomials of the potential. For SL_n\, there i s an algorithm due to Gleizer and Postnikov which gets all monomials of th e Berenstein-Kazhdan potential using combinatorics of wiring diagrams. For this case\, our algorithm uses simpler combinatorics and is faster than t he Gleizer-Postnikov algorithm. The cluster algorithm due to Genz\, Schuma nn and me is polynomial in time but it uses divisions of polynomials of se veral variables.\nIf time permits I will report on applications of decorat ed graphs to analysis of the Newton polytopes of F-polynomials related to the Gross-Hacking-Keel-Kontsevich potentials. The talk is based on joint works with Volker Genz and Bea Schumann and with Yuki Kanakubo and Toshiki Nakashima.\n\nThis talk will take place in hybrid mode at the IHP.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Vasserot (Paris Cité) DTSTART;VALUE=DATE-TIME:20230417T120000Z DTEND;VALUE=DATE-TIME:20230417T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/128 DESCRIPTION:Title: Critical convolution algebras and quantum loop grou ps\nby Eric Vasserot (Paris Cité) as part of Paris algebra seminar\n\ n\nAbstract\nWe introduce a new family of algebras attached to quivers wit h potentials\, using critical K-theory and critical Borel-Moore homology. They generalize the convolution algebras attached to quivers by Nakajima. We give some applications to cohomological and K-theoretical Hall algebras \, to shifted quantum loop groups\, and to Kirillov-Reshetikhin and prefun damental representations. \n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Owen Garnier (Amiens) DTSTART;VALUE=DATE-TIME:20230424T120000Z DTEND;VALUE=DATE-TIME:20230424T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/129 DESCRIPTION:Title: Homology of a category and the Dehornoy-Lafont orde r complex\nby Owen Garnier (Amiens) as part of Paris algebra seminar\n \n\nAbstract\nThe work of Squier and Kobayashi proves that the homology of a monoid can be computed using a so called complete rewriting system\, wh ich acts as a convenient presentation of the monoid.\n\nLater\, Dehornoy a nd Lafont noted that such a convenient presentation arises in particular w hen considering monoids satisfying combinatorial assumptions regarding exi stence of lcms. This gave rise to the so called Dehornoy-Lafont order comp lex\, which was used to compute the homology of complex braid groups by Ca llegaro and Marin.\n\nAfter giving a quick summary of these works\, I will present a generalization of this latter complex to the case of a category which again satisfies convenient combinatorial assumptions. \n\nOf course \, as my "true" goal is to compute the homology of a group using some asso ciated category\, I will also give a link between the homology of a catego ry\, that of its enveloping groupoid\, and that of a group which is equiva lent to the said groupoid.\n\nLastly\, I will explain an application to th e case of the complex braid group $B_{31}$\, which is studied through its associated Garside category\, and which was not directly covered by previo us approaches.\n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/12 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Frédéric Chapoton (CNRS Strasbourg) DTSTART;VALUE=DATE-TIME:20230619T120000Z DTEND;VALUE=DATE-TIME:20230619T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/130 DESCRIPTION:Title: Posets and fractional Calabi-Yau categories\nby Frédéric Chapoton (CNRS Strasbourg) as part of Paris algebra seminar\n\ n\nAbstract\nIn combinatorics\, several famous enumeration results involve a special kind of product formula. The very same kind of product formula gives the Milnor number of an isolated quasi-homogenous singularity. It se ems possible that one could relate combinatorics and singularities by mean s of derived categories: on the one hand\, modules over incidence algebras of partially ordered sets (posets) and on the other hand\, some kind of F ukaya-like category that should categorify the Milnor fibration. Even if p art of this remains very unprecise and vague\, this implies many concrete conjectures about derived equivalences between posets. \n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Bershtein (Moscow and IPMU) DTSTART;VALUE=DATE-TIME:20230508T120000Z DTEND;VALUE=DATE-TIME:20230508T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/131 DESCRIPTION:Title: Cluster Hamiltonian reductions: examples\nby Mi khail Bershtein (Moscow and IPMU) as part of Paris algebra seminar\n\n\nAb stract\nI will talk about an\, in general conjectural\, construction of a X-cluster structure on certain Hamiltonian reduction of a X-cluster variet y. There are two main classes of examples of such constructions: moduli sp aces of framed local systems with special monodromies and phase spaces of Goncharov-Kenyon integrable systems. The first class includes the phase sp ace of open XXZ chain and Ruijsenaars integrable systems. The second class includes integrable systems corresponding to the q-difference Painleve eq uations.\n\nBased on works in progress and discussions with P. Gavrylenko\ , A. Marshakov\, M. Semenyakin\, A. Shapiro\, G. Schrader.\n\nThis talk wi ll take place on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Haibo Jin (Cologne) DTSTART;VALUE=DATE-TIME:20230515T120000Z DTEND;VALUE=DATE-TIME:20230515T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/132 DESCRIPTION:Title: A complete derived invariant and silting theory for graded gentle algebras\nby Haibo Jin (Cologne) as part of Paris algeb ra seminar\n\n\nAbstract\nWe show that among the derived equivalent classe s of homologically smooth and proper graded gentle algebras there is only one class whose perfect derived category does not admit silting objects.\n \nAs one application we give a sufficient and necessary condition for any homologically smooth and proper graded gentle algebra under which all pre -silting objects in its perfect derived category may be complete into silt ing objects.\n\nAs another application we confirm a conjecture by Lekili a nd Polishchuk that the geometric invariants which they construct for homol ogically smooth and proper graded gentle algebras are a complete derived i nvariant. Hence\, we obtain a complete invariant for partially wrapped Fuk aya categories of surfaces with stops. \n\nThis is a report on joint work with Sibylle Schroll and Zhengfang Wang.\n\nThis talk will take place in h ybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonid Positselski (Prague) DTSTART;VALUE=DATE-TIME:20230522T121500Z DTEND;VALUE=DATE-TIME:20230522T131500Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/133 DESCRIPTION:Title: The homomorphism removal and repackaging constructi on\nby Leonid Positselski (Prague) as part of Paris algebra seminar\n\ n\nAbstract\nThis work is an attempt to understand the maximal natural gen erality context for\nthe Koenig-Kuelshammer-Ovsienko construction in the t heory of quasi-hereditary algebras by\nputting it into a category-theoreti c context. Given a field k and a k-linear exact category E \nwith a chosen set of nonzero objects F_i such that every object of E is a finitely iter ated \nextension of some F_i\, we construct a coalgebra C whose irreducibl e comodules L_i are indexed by the same indexing set\, and an exact functo r from C-comod to E taking L_i to F_i such that the spaces Ext^n between L _i in C−comod are the same as between F_i in E (for n > 0). Thus\, the a belian category C−comod is obtained from the exact category E by removin g all the nontrivial homomorphisms between the chosen objects F_i in E whi le keeping the Ext spaces unchanged. The removed homomorphisms are then re packaged into a semialgebra S over C such that the exact category E can be recovered as the category of S-semimodules induced from finite-dimensiona l C-comodules. The construction used Koszul duality twice: once as absolut e and once as relative Koszul duality.\n\n\nThis talk will take place in h ybrid format at the GAP conference at the Institut Henri Poincaré\, cf. < a href="https://personal.psu.edu/mps16/hirsutes2023/gap2023.html">GAP. \n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine De Saint Germain (Hong Kong U.) DTSTART;VALUE=DATE-TIME:20230612T120000Z DTEND;VALUE=DATE-TIME:20230612T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/134 DESCRIPTION:Title: Cluster additive functions and acyclic cluster alge bras\nby Antoine De Saint Germain (Hong Kong U.) as part of Paris alge bra seminar\n\n\nAbstract\nIn his study of combinatorial features of clust er categories and cluster-tilted algebras\, Ringel introduced an analogue of additive functions of stable translation quivers called cluster-additiv e functions. \n\nIn this talk\, we will define cluster-additive functions associated to any acyclic mutation matrix\, relate them to tropical point s of the cluster X-variety\, and realise their values as certain compatibi lity degrees between functions on the cluster A-variety associated to the Langlands dual mutation matrix (in accordance with the philosophy of Fock- Goncharov). This is based on joint work with Peigen Cao and Jiang-Hua Lu. \n\nThis talk will take place in hybrid mode at the Institut Henri Poincar é.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Rivera (Purdue) DTSTART;VALUE=DATE-TIME:20230626T120000Z DTEND;VALUE=DATE-TIME:20230626T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/135 DESCRIPTION:Title: Loop spaces and bialgebras\nby Manuel Rivera (P urdue) as part of Paris algebra seminar\n\n\nAbstract\nI will discuss seve ral interlocked constructions giving rise to bialgebra structures all of w hich have parallel algebraic and topological interpretations. The bialgebr as considered will be of different flavors depending on the compatibility between the product and coproduct\; for instance\, we will see examples of Hopf\, Frobenius\, infinitesimal and Lie bialgebras. These structures app ear when analyzing the role of loop spaces in homotopy theory and manifold topology and reveal new results regarding the algebraic nature of geometr ic space.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Duncan Laurie (Oxford) DTSTART;VALUE=DATE-TIME:20231002T120000Z DTEND;VALUE=DATE-TIME:20231002T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/136 DESCRIPTION:Title: Quantum toroidal algebras: braid group actions\, au tomorphisms\, and representation theory\nby Duncan Laurie (Oxford) as part of Paris algebra seminar\n\n\nAbstract\nQuantum toroidal algebras Uq( g_tor) occur as the Drinfeld\nquantum affinizations of quantum affine alge bras. In particular\; they\ncontain (and are generated by) a horizontal an d vertical copy of the\naffine quantum group. In type A\, Miki obtained an automorphism of\nUq(g_tor) exchanging these subalgebras\, which has since played a\ncrucial role in the investigation of its structure and represen tation\ntheory.\n\nIn this talk\; we shall construct an action of the exte nded double\naffine braid group B on the quantum toroidal algebra in all u ntwisted\ntypes. In the simply laced cases\, using this action and certain \ninvolutions of B we obtain automorphisms and anti-automorphisms of\nUq(g _tor) which exchange the horizontal and vertical subalgebras\, thus\ngener alising the results of Miki. We shall then discuss potential\nextensions o f these results\, and applications to the representation\ntheory of quantu m toroidal algebras.\n\nThis talk will take place in hybrid mode at the In stitut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 6/ END:VEVENT BEGIN:VEVENT SUMMARY:Bill Crawley-Boevey (Bielefeld) DTSTART;VALUE=DATE-TIME:20230713T120000Z DTEND;VALUE=DATE-TIME:20230713T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/137 DESCRIPTION:Title: Integral representations of quivers\nby Bill Cr awley-Boevey (Bielefeld) as part of Paris algebra seminar\n\n\nAbstract\nI n the 1990s\, I classified rigid representations of a quiver by finitely g enerated free modules over a principal ideal ring. I shall extend the resu lts to representations of a quiver by finitely generated projective module s over an arbitrary commutative ring. \n\nThis talk will kindly be shared by the organisation of the conference \nHomological algebra and representation theor y. It will take place in hybrid mode at Karlovasi (Samos\, Greece).\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Thomas (Heidelberg) DTSTART;VALUE=DATE-TIME:20231127T130000Z DTEND;VALUE=DATE-TIME:20231127T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/138 DESCRIPTION:Title: A q-deformation of sl2 and the Witt algebra\nby Alexander Thomas (Heidelberg) as part of Paris algebra seminar\n\n\nAbstr act\nI will present new q-deformations of Lie algebras linked to the modul ar group and the q-rational numbers as defined by Morier-Genoud and Ovsien ko. In particular\, I will describe deformations of sl2 and the Witt algeb ra. These deformations are realized as differential operators acting on th e hyperbolic plane\, giving new insights into q-rationals. \n\nThis talk w ill take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Norihiro Hanihara (IPMU) DTSTART;VALUE=DATE-TIME:20231023T120000Z DTEND;VALUE=DATE-TIME:20231023T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/139 DESCRIPTION:Title: Silting-cluster tilting correspondences\nby Nor ihiro Hanihara (IPMU) as part of Paris algebra seminar\n\n\nAbstract\nClus ter categories are fundamental objects in representation theory\, includin g such topics as cluster algebras\, tilting theory\, singularity theory. T he theory of Amiot\, Guo\, and Keller shows that tilting/silting objects i n derived categories (of a finite dimensional algebra or of a Calabi-Yau d g algebra) give rise to cluster tilting objects in the cluster category. W e study such correspondences between silting objects and cluster tilting o bjects. We propose a conjecture on the liftability of cluster tilting obje cts in the cluster category to silting objects\, and discuss some evidence for it. This is based on a joint work with Osamu Iyama.\n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/13 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Se-jin Oh (Sungkyunkwan U.) DTSTART;VALUE=DATE-TIME:20231016T120000Z DTEND;VALUE=DATE-TIME:20231016T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/140 DESCRIPTION:Title: A noncommutative algebra arising from the $t$-quant ized Cartan matrix\nby Se-jin Oh (Sungkyunkwan U.) as part of Paris al gebra seminar\n\n\nAbstract\nThe quantum Cartan matrix appears ubiquitousl y as a key combinatorial ingredient in the representation theory of quantu m affine algebras. Through the generalized Schur-Weyl duality\, it also pl ays a central role in the one of quiver Hecke algebras and the quantum uni potent coordinate ring of (skew-)symmetric finite type. Even though there are quiver Hecke algebras and quantum unipotent coordinate rings of non (s kew-)symmetric finite type\, there is no counterpart in representation the ory as far as I and my collaborators understand.\nIn this talk\, I introdu ce a non-commutative ring over $\\Q(q^{1/2}$)\, which is expected to be a quantum Grothendieck ring for a Hernandez-Leclerc category\, if such a rep resentation theory exists\, by using the t-quantized Cartan matrix. When w e consider its heart subalgebra\, the algebra is isomorphic to the quantu m unipotent coordinate ring of any finite type.\nThis talk is mainly based on joint work with Kashiwara\, Jang and Lee.\n\nThis talk will take place on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Fan Qin (Shanghai Jiaotong) DTSTART;VALUE=DATE-TIME:20231009T120000Z DTEND;VALUE=DATE-TIME:20231009T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/141 DESCRIPTION:Title: Analogs of dual canonical bases for cluster algebra s from Lie theory\nby Fan Qin (Shanghai Jiaotong) as part of Paris alg ebra seminar\n\n\nAbstract\nThe (quantized) coordinate rings of many inter esting varieties from Lie theory are (quantum) cluster algebras. We constr uct the common triangular bases for these algebras. Such bases provide ana logs of the dual canonical bases\, whose existence has been long expected in cluster theory. For symmetric Cartan matrices\, they are positive and a dmit monoidal categorification after base change. We employ a unified appr oach based on cluster algebra operations. Our results apply to algebraic g roups\, double Bott-Samelson cells\, and braid varieties\, etc. Additional ly\, we find applications in representations of quantum affine algebras.\n \nThis talk will take place on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Merlin Christ (IMJ-PRG) DTSTART;VALUE=DATE-TIME:20231106T130000Z DTEND;VALUE=DATE-TIME:20231106T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/142 DESCRIPTION:Title: Relative Calabi-Yau structures and extriangulated c luster categories\nby Merlin Christ (IMJ-PRG) as part of Paris algebra seminar\n\n\nAbstract\nWe will begin with an introduction to relative Cal abi-Yau structures in the sense of Brav-Dyckerhoff\, generalizing the noti on of a Calabi-Yau triangulated (or dg-) category to functors. Via so-call ed relative theory\, Calabi-Yau functors give rise to extriangulated categ ories\, which are Frobenius 2-Calabi-Yau. We apply this to examples of clu ster categories of surfaces\, categorifying the surface cluster algebras w ith coefficients in the boundary arcs. This talk is mostly based on my pre print arXiv:2209.06595. \n\nThis talk will take place in hybrid mode at th e Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Francone (Lyon) DTSTART;VALUE=DATE-TIME:20231113T130000Z DTEND;VALUE=DATE-TIME:20231113T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/143 DESCRIPTION:Title: Minimal monomial lifting of cluster algebras and br anching problems\nby Luca Francone (Lyon) as part of Paris algebra sem inar\n\n\nAbstract\nThe minimal monomial lifting is a sort of homogenisati on technique\, whose goal is to identify a cluster algebra structure on ce rtain "suitable for lifting" schemes\, compatibly with a base cluster stru cture on a distinguished subscheme. This technique allows to recover\, by geometric methods\, some well known cluster structures. In this talk\, we will present this technique and discuss applications to branching problems in representation theory of complex reductive groups.\n\nThis talk will t ake place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Wahei Hara (IPMU) DTSTART;VALUE=DATE-TIME:20231120T130000Z DTEND;VALUE=DATE-TIME:20231120T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/144 DESCRIPTION:Title: Spherical objects in dimension two and three\nb y Wahei Hara (IPMU) as part of Paris algebra seminar\n\n\nAbstract\nIn thi s talk\, we discuss the classification problem of spherical “like” obj ects in various geometric settings including the minimal resolution of an ADE surface singularity and a 3-fold flopping contraction. The classificat ion of spherical objects is related to questions about the autoequivalence groups or Bridgeland stability conditions\, but in 3-fold settings\, this is not always a correct problem to ask. In the first half of the talk\, w e discuss what kind of objects should be classified\, and in the second ha lf\, a sketch of the proof will be explained. Our new technique can also b e applied to the heart of a bounded t-structure\, and classifies all t-str uctures of the associated null category. As a corollary\, the connectednes s of the space of stability conditions follows. This is all joint work wit h Michael Wemyss.\n\nThis talk will take place on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonah Berggren (Kentucky) DTSTART;VALUE=DATE-TIME:20231204T130000Z DTEND;VALUE=DATE-TIME:20231204T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/145 DESCRIPTION:Title: Consistent Dimer Models on Surfaces with Boundary\nby Jonah Berggren (Kentucky) as part of Paris algebra seminar\n\n\nAbs tract\nA dimer model is a quiver with faces embedded in a surface. Dimer m odels on the disk and torus are particularly well-studied\, though these t heories have remained largely separate. Various “consistency conditions ” may be imposed on dimer models on the disk or torus with implications relating to 3-Calabi-Yau properties and categorification.\n \nWe extend ma ny of these definitions and results to the setting of general surfaces wit h boundary. We show that the completed dimer algebra of a “strongly cons istent” dimer model is bimodule internally 3-Calabi-Yau with respect to its boundary idempotent. As a consequence\, the Gorenstein-projective modu le category of the completed boundary algebra of a suitable dimer model ca tegorifies the cluster algebra given by its underlying ice quiver. We give a class of examples of annulus models satisfying the requisite conditions . \n\nThis talk will take place on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Melissa Sherman-Bennett (MIT) DTSTART;VALUE=DATE-TIME:20231218T130000Z DTEND;VALUE=DATE-TIME:20231218T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/146 DESCRIPTION:Title: Cluster structures on braid and Richardson varietie s\nby Melissa Sherman-Bennett (MIT) as part of Paris algebra seminar\n \n\nAbstract\nIn 2014\, Leclerc gave a construction of a conjectural clust er structure on open Richardson varieties in types ADE. His construction w as categorical in nature\, involving preprojective algebra modules. His co njecture inspired work on cluster structures on braid varieties in arbitra ry type\, which generalize open Richardsons. Two cluster structures on bra id varieties were recently constructed. The first one\, based on ideas and techniques from symplectic topology\, is due to Casals-Gorsky-Gorsky-Le-S hen-Simental. I will discuss the other\, which is joint work with Galashin \, Lam and Speyer. Our main geometric tool is the Deodhar decomposition. I n type A\, our quivers are given by "3D plabic graphs"\, which generalize Postnikov's plabic graphs for the Grassmannian. Time permitting\, I will a lso discuss related work with Serhiyenko\, where we show that for type A R ichardsons\, Leclerc's conjectural categorical construction does in fact g ive a cluster structure\, with quivers again given by 3D plabic graphs.\n\ nThis talk will be on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 6/ END:VEVENT BEGIN:VEVENT SUMMARY:JiaRui Fei (Shanghai Jiao Tong) DTSTART;VALUE=DATE-TIME:20231211T130000Z DTEND;VALUE=DATE-TIME:20231211T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/147 DESCRIPTION:Title: Crystal Structure of Upper Cluster Algebras\nby JiaRui Fei (Shanghai Jiao Tong) as part of Paris algebra seminar\n\n\nAbs tract\nWe describe the upper seminormal crystal structure for the $\\mu$-s upported $\\delta$-vectors for any quiver with potential with reachable fr ozen vertices\, or equivalently for the tropical points of the correspondi ng cluster $\\mathcal{X}$-variety. We show that the crystal structure can be algebraically lifted to the generic basis of the upper cluster algebra. This can be viewed as an additive categorification of the crystal structu re arising from cluster algebras. We introduce the biperfect bases and the strong biperfect bases in the cluster algebra setting and give a descript ion of all strong biperfect bases.\n\nThis talk will be on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Johan Asplund (Stony Brook U.) DTSTART;VALUE=DATE-TIME:20240115T130000Z DTEND;VALUE=DATE-TIME:20240115T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/148 DESCRIPTION:Title: Relative Ginzburg algebras and Chekanov-Eliashberg dg-algebras\nby Johan Asplund (Stony Brook U.) as part of Paris algebr a seminar\n\n\nAbstract\nThe Chekanov-Eliashberg dg-algebra yields a power ful isotopy invariant of (possibly singular) Legendrian submanifolds in a class of contact manifolds\, and is also intimately related to Fukaya cate gories of a class of non-compact symplectic manifolds. The goal for this t alk is to explain how the relative Ginzburg algebra associated to any ice quiver with trivial potential is quasi-isomorphic to some Chekanov-Eliashb erg dg-algebra. The proof is constructive. I will give a gentle introducti on to Chekanov-Eliashberg dg-algebras and will discuss how the relation to relative Ginzburg algebras is interesting to contact and symplectic geome ters.\n\nThis talk will be on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Fan Qin (Beijing Normal) DTSTART;VALUE=DATE-TIME:20240122T130000Z DTEND;VALUE=DATE-TIME:20240122T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/149 DESCRIPTION:Title: Applications of the freezing operators on cluster a lgebras\nby Fan Qin (Beijing Normal) as part of Paris algebra seminar\ n\n\nAbstract\nWe utilize freezing operators to establish connections amon g distinct (quantum) upper cluster algebras. This approach enables us to c ompare the quantized coordinate rings of different varieties. We prove tha t these operators send localized (quantum) cluster monomials to localized (quantum) cluster monomials. Furthermore\, in many instances\, they also p reserve bases. Remarkably\, the bases constructed via freezing operators c oincide with those obtained via localization.\n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/14 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Sabin Cautis (U. of British Columbia) DTSTART;VALUE=DATE-TIME:20240311T130000Z DTEND;VALUE=DATE-TIME:20240311T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/150 DESCRIPTION:Title: Categorical cluster structure of Coulomb branches\nby Sabin Cautis (U. of British Columbia) as part of Paris algebra semi nar\n\n\nAbstract\nCoulomb branches are certain moduli spaces arising in s upersymmetric field theory. They include as special cases many spaces of i ndependent interest such as double affine Hecke algebras\, certain open Ri chardson varieties\, multiplicative Nakajima quiver varieties etc. In the four-dimensional case\, one expects that their coordinate rings can be cat egorified by abelian monoidal categories carrying a cluster structure.\n\n After reviewing the mathematical construction of these Coulomb branches we will explain how these categories are constructed and why the cluster str ucture appears. This is joint work with Harold Williams. \n\n\n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Till Wehrhan (Bonn) DTSTART;VALUE=DATE-TIME:20240129T130000Z DTEND;VALUE=DATE-TIME:20240129T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/151 DESCRIPTION:Title: Chevalley-Monk formulas for bow varieties\nby T ill Wehrhan (Bonn) as part of Paris algebra seminar\n\n\nAbstract\nThe the ory of stable envelopes\, introduced by Maulik and Okounkov\, provides a f ascinating interplay between the geometry of holomorphic symplectic variet ies and integrable systems. We apply this theory to bow varieties which fo rm a rich family of holomorphic symplectic varieties including type A Naka jima quiver varieties. We then discuss a formula for the multiplication of torus equivariant first Chern classes of tautological bundles of bow vari eties with respect to the stable envelope basis. This formula naturally ge neralizes the classical Chevalley-Monk formula and can be expressed in ter ms of moves on skein-type diagrams that label the stable envelope basis. \ n\nThis talk will take place in hybrid mode at the Institut Henri Poincar é.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Dirceu Bagio (Fed. U. of Santa Catarina) DTSTART;VALUE=DATE-TIME:20240108T130000Z DTEND;VALUE=DATE-TIME:20240108T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/152 DESCRIPTION:Title: Tameness of a restricted enveloping algebra\nby Dirceu Bagio (Fed. U. of Santa Catarina) as part of Paris algebra seminar \n\n\nAbstract\nWe will describe a 5-dimensional Lie algebra over an algeb raically\nclosed field of characteristic 2 and show that its restricted en veloping algebra is special biserial\, hence tame. We obtain an explicit d escription of all of its families of finite-dimensional indecomposable mod ules using Crawley-Boevey's description via strings and bands of the indec omposable modules over a special biserial algebra. This is joint work with N. Andruskiewitsch\, S. D. Flora and D. Flores.\n\nThis talk will take pl ace in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Geoffrey Janssens (UCLouvain) DTSTART;VALUE=DATE-TIME:20240212T130000Z DTEND;VALUE=DATE-TIME:20240212T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/153 DESCRIPTION:Title: Group invariants observed through a representation- theoretical lens\nby Geoffrey Janssens (UCLouvain) as part of Paris al gebra seminar\n\n\nAbstract\nThe leitfaden of this talk will be the genera l problem of determining which invariants of a finite group G are determin ed by which piece of the representation category of G over a commutative r ing R. In the first part of the talk\, we will recall the information enco ded by the monoidal category of complex representations and its (braided) auto-equivalences. By doing so we will stumble on a question concerning th e connection between two types of rigidity associated to G. The first is g iven by the group of class-preserving outer automorphisms of G and the sec ond is a birational invariant of the quotient variety V/G\, where V is a f aithful representation of G. The aim of the second part of the talk will b e to present some new perspective on them. Thereafter\, in the last part\, we will explain how the situation changes when taking R to be a number fi eld or its ring of integers. In particular\, the role of the theory of ari thmetic groups will be emphasized. All along the talk\, we will mention so me open questions and some recent contributions.\n\nThis talk will take pl ace in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiaofa Chen (USTC Hefei) DTSTART;VALUE=DATE-TIME:20240205T130000Z DTEND;VALUE=DATE-TIME:20240205T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/154 DESCRIPTION:Title: Exact dg categories and higher Auslander correspond ences\nby Xiaofa Chen (USTC Hefei) as part of Paris algebra seminar\n\ n\nAbstract\nExact dg categories allow to enhance extriangulated categorie s and\nto perform constructions like functor categories or tensor products \nfor which the extriangulated structure alone does not suffice.\nIn parti cular\, they yield a new approach to and a generalization\nof higher versi ons of Auslander correspondences as established\nby Iyama and by Iyama-Sol berg\, for example. In this talk\, I will give \nan introduction to exact dg categories and sketch their application\nto correspondences on the exam ple of 0-Auslander categories. \nWe will see in particular that the framew ork of exact dg\ncategories allows to enhance the correspondences to equiv alences\nof infinity-groupoids.\n\nThis talk will take place on Zoom only. \n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu Qiu (Tsinghua) DTSTART;VALUE=DATE-TIME:20240226T130000Z DTEND;VALUE=DATE-TIME:20240226T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/156 DESCRIPTION:Title: On cluster braid groups\nby Yu Qiu (Tsinghua) a s part of Paris algebra seminar\n\n\nAbstract\nWe introduce cluster braid groups\, with motivations coming from the study of stability conditions on triangulated categories. In the Coxeter-Dynkin case\, they are naturally isomorphic to the corresponding Artin braid groups (1407.5986 and 2310.028 71). In the surface case\, they are naturally isomorphic to braid twist gr oups (1407.0806\, 1703.10053 and 1805.00030). If time permits\, I will men tion an application to quadratic differentials.\n\nThis talk will take pla ce on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Williams (Lancaster) DTSTART;VALUE=DATE-TIME:20240318T130000Z DTEND;VALUE=DATE-TIME:20240318T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/157 DESCRIPTION:Title: Donaldson--Thomas invariants for the Bridgeland--Sm ith correspondence\nby Nicholas Williams (Lancaster) as part of Paris algebra seminar\n\n\nAbstract\nCelebrated work of Bridgeland and Smith sho ws a correspondence between quadratic differentials on Riemann surfaces an d stability conditions on certain 3-Calabi--Yau triangulated categories. P art of this correspondence is that finite-length trajectories of the quadr atic differential correspond to stable objects of phase 1. Speaking roughl y\, these stable objects are then counted by an associated Donaldson--Thom as invariant. Work of Iwaki and Kidwai predicts particular values for thes e Donaldson--Thomas invariants according to the different types of finite- length trajectories\, based on the output of topological recursion. We sho w that the category recently studied by Christ\, Haiden\, and Qiu produces Donaldson--Thomas invariants matching these predictions. This is joint wo rk with Omar Kidwai.\n\nThis talk will take place in hybrid mode at the In stitut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Wedrich (Hamburg) DTSTART;VALUE=DATE-TIME:20240513T120000Z DTEND;VALUE=DATE-TIME:20240513T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/158 DESCRIPTION:Title: A braided monoidal (infinity\,2)-category from link homology\nby Paul Wedrich (Hamburg) as part of Paris algebra seminar\ n\n\nAbstract\nAn early highlight of quantum topology was the observation that the Jones polynomial -- and many other knot and link invariants -- ar ise from braided monoidal categories of quantum group representations. In hindsight\, this can be understood as underlying reason for the existence of associated topological quantum field theories (TQFTs) in 3 and 4 dimens ions.\n\nNot much later\, Khovanov discovered a link homology theory that categorifies the Jones polynomial. It associates graded chain complexes to links\, from which the Jones polynomials can be recovered. It was therefo re speculated that Khovanov homology and its variants may themselves be ex pressible in terms of certain braided monoidal 2-categories and that there should exist associated TQFTs in 4 and 5 dimensions that may be sensitive to smooth structure.\n\nA major challenge in fully realizing this dream i s the problem of coherence: Link homology theories live in the world of ho mological algebra\, where constructing a braided monoidal structure in pri nciple requires an infinite amount of higher and higher homological cohere nce data. In this talk\, I will sketch a proposed solution to this problem \, joint with Leon Liu\, Aaron Mazel-Gee\, David Reutter\, and Catharina S troppel\, and explain how we use the language of infinity-categories to bu ild an E2-monoidal (infinity\,2)-category which categorifies the Hecke bra ided monoidal category underlying the HOMFLYPT link polynomial.\n\n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitriy Voloshyn (Pohang) DTSTART;VALUE=DATE-TIME:20240408T120000Z DTEND;VALUE=DATE-TIME:20240408T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/159 DESCRIPTION:Title: Generalized cluster structures on the special linea r group\nby Dmitriy Voloshyn (Pohang) as part of Paris algebra seminar \n\n\nAbstract\nThe Gekhtman-Shapiro-Vainshtein conjecture (the GSV conjec ture) states that for any any given simple complex algebraic group G and a ny Poisson bracket from the Belavin-Drinfeld class\, there exists a compat ible generalized cluster structure. In this talk\, I will review the proce ss of constructing compatible generalized cluster structures\, as well as the current state-of-the-art on the GSV conjecture. After that\, I will de scribe a construction of generalized cluster structures on SL_n compatible with Poisson brackets induced from the Poisson dual of SL_n endowed with the Poisson structure determined by a BD triple of\ntype A_{n-1}. I will a lso describe the associated family of birational quasi-isomorphisms. The t alk will be based on the preprint arXiv:2312.04859 (joint work with M. Gek htman). \n\nThis talk will take place on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/15 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Hussein Mourtada (U. Paris Cité) DTSTART;VALUE=DATE-TIME:20240325T130000Z DTEND;VALUE=DATE-TIME:20240325T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/160 DESCRIPTION:Title: Singularities of algebraic varieties and integer pa rtitions\nby Hussein Mourtada (U. Paris Cité) as part of Paris algebr a seminar\n\n\nAbstract\nI will talk about a link between arc spaces of si ngularities\, which are algebro-geometric objects\, and identities of inte ger partitions.\n\nThis link allows us to discover new partition identitie s in the spirit of the work of Ramanujan. The talk is accessible to a wide audience. \n\nThis talk will take place in hybrid mode at the Institut He nri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Tiago Cruz (Stuttgart) DTSTART;VALUE=DATE-TIME:20240422T120000Z DTEND;VALUE=DATE-TIME:20240422T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/161 DESCRIPTION:Title: Relative Auslander-Gorenstein pairs\nby Tiago C ruz (Stuttgart) as part of Paris algebra seminar\n\n\nAbstract\nA famous r esult in representation theory is Auslander’s correspondence which conne cts finite-dimensional algebras of finite representation-type with Ausland er algebras. Over the years\, many generalisations of Auslander algebras h ave been proposed: for instance n-Auslander algebras (by Iyama)\, n-minima l Auslander–Gorenstein algebras (by Iyama and Solberg)\, among others. A ll of the concepts above require the existence of a faithful projective-in jective module and use classical dominant dimension. Now replace the faith ful projective-injective module with a self-orthogonal module and classica l dominant dimension with relative dominant dimension with respect to a mo dule and you get a relative Auslander-Gorenstein pair.\n\nIn this talk\, w e introduce relative Auslander-Gorenstein pairs. Further\, we will charact erise relative Auslander pairs (those whose underlying algebras have finit e global dimension) by the existence and uniqueness of tilting-cotilting m odules having the highest values of relative dominant and codominant dimen sion with respect to the self-orthogonal module. At the end\, we discuss e xplicit examples of relative Auslander pairs. (This is joint work with Chr ysostomos Psaroudakis.)\n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Robalo (Sorbonne U.) DTSTART;VALUE=DATE-TIME:20240429T120000Z DTEND;VALUE=DATE-TIME:20240429T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/162 DESCRIPTION:Title: Choices of HKR isomorphisms and exponential maps\nby Marco Robalo (Sorbonne U.) as part of Paris algebra seminar\n\n\nAbs tract\nIn this talk\, I will explain a computation describing the space of choices of functorial HKR isomorphisms as choices of exponential maps fro m the additive to the multiplicative formal group. This computation uses t he construction of a filtered circle obtained in collaboration with with M oulinos and Toën\, which combines the HKR filtration and the circle actio n on Hochschild homology even when the characteristic of the base field is positive. We will review the construction of the filtered circle and the relation with Witt vectors.\n\nThis talk will take place in hybrid mode a t the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Reineke DTSTART;VALUE=DATE-TIME:20240506T120000Z DTEND;VALUE=DATE-TIME:20240506T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/163 DESCRIPTION:Title: Floer potentials\, cluster algebras and quiver repr esentations\nby Markus Reineke as part of Paris algebra seminar\n\n\nA bstract\nWe interpret Floer potentials (encoding certain Gromov-Witten inv ariants) of "exotic" monotone Lagrangian tori in dle Pezzo surfaces as clu ster characters of representations of certain quivers with potential.\n\nT his talk will be on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Merlin Christ (Paris) DTSTART;VALUE=DATE-TIME:20240304T130000Z DTEND;VALUE=DATE-TIME:20240304T140000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/164 DESCRIPTION:Title: Complexes of stable infinity-categories and pervers e schobers\nby Merlin Christ (Paris) as part of Paris algebra seminar\ n\n\nAbstract\nA complex of stable infinity-categories is a categorificati on of a chain complex\, meaning a sequence of stable infinity-categories t ogether with a differential that squares to the zero functor. Examples of such categorical complexes arise for instance via a categorification of th e totalization construction\, which produces a categorical complex from a categorical multi-complex\, such as a commuting cube of stable infinity-ca tegories. We will then explain how categorified perverse sheaves\, also kn own as perverse schobers\, on C^n (with a certain stratification) can be d escribed in terms of categorical cubes and categorical complexes of spheri cal functors\, and what categorical totalization means in this case geomet rically. This talk is based on joint work with T. Dyckerhoff and T. Walde. \n\nThis talk will take place in hybrid mode at the Institut Henri Poinca ré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 4/ END:VEVENT BEGIN:VEVENT SUMMARY:David Pauksztello (Lancaster) DTSTART;VALUE=DATE-TIME:20240527T120000Z DTEND;VALUE=DATE-TIME:20240527T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/165 DESCRIPTION:Title: Convex geometry for (co)fans of abelian categories< /a>\nby David Pauksztello (Lancaster) as part of Paris algebra seminar\n\n \nAbstract\nArising in cluster theory\, the g-vector fan is a convex geome tric invariant encoding the mutation behaviour of clusters. In representat ion theory\, the g-vector fan encodes the mutation theory of support tau-t ilting objects or\, equivalently\, two-term silting objects. In this talk\ , we will describe a generalisation of the g-vector fan which in some sens e “completes” the g-vector fan: the heart fan of an abelian category. This convex geometric invariant encodes many important homological propert ies: e.g. one can detect from the convex geometry whether an abelian categ ory is length\, whether it has finitely many torsion pairs\, and whether a given Happel-Reiten-Smaloe tilt is length. This talk will be a report on joint work with Nathan Broomhead\, David Ploog and Jon Woolf.\n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Pressland (Glasgow) DTSTART;VALUE=DATE-TIME:20240617T120000Z DTEND;VALUE=DATE-TIME:20240617T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/166 DESCRIPTION:Title: Categorical cluster ensembles\nby Matthew Press land (Glasgow) as part of Paris algebra seminar\n\n\nAbstract\nIn their ge ometric approach to cluster theory\, Fock–Goncharov and Gross–Hacking –Keel construct cluster varieties beginning with a seed datum. This cons ists of a lattice which contains various distinguished sublattices\, has a preferred basis\, and carries a partially defined bilinear form. A proces s of mutation allows one to construct more such seed data\, and birational gluing maps between the tori dual to the lattices\, leading to two cluste r varieties known as A and X. By enhancing the initial data to a cluster e nsemble\, in which the bilinear form is extended to the whole lattice\, on e also obtains a map from A to X.\nIn this talk\, based on joint work with Jan Grabowski\, I will explain how one can obtain a seed datum\, and in m any cases a full cluster ensemble\, from each cluster-tilting subcategory of an appropriate 2-Calabi–Yau category. Furthermore\, I will explain ho w the seed data of different cluster-tilting subcategories are related\, g eneralising the relationship between a seed datum and its mutations.\n\nTh is talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 6/ END:VEVENT BEGIN:VEVENT SUMMARY:Théo Pinet (Paris Cité) DTSTART;VALUE=DATE-TIME:20240624T120000Z DTEND;VALUE=DATE-TIME:20240624T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/167 DESCRIPTION:Title: Inflations for representations of shifted quantum a ffine algebras\nby Théo Pinet (Paris Cité) as part of Paris algebra seminar\n\n\nAbstract\nThe only finite-dimensional simple Lie algebra admi tting a 2-dimensional irreducible representation is sl(2). The restriction functors arising from Dynkin diagram inclusions in (classical) Lie theory are thus in general not essentially surjective on finite-dimensional simp le modules. The goal of this talk is to specify whether or not this "surje ctivity defect" remains in the case of Finkelberg-Tsymbaliuk's shifted qua ntum affine algebras (SQAAs).\n\nSQAAs are infinite-dimensional associativ e algebras parametrized by a simple finite-dimensional Lie algebra and a c oweight in the corresponding coweight lattice. They appear naturally in th e study of Coulomb branches\, of quantum integrable systems and of cluster algebras. In this presentation\, we will give a brief introduction to the vast representation theory of SQAAs and will state some results about the existence of remarkable modules\, that we call "inflations"\, which are c onstructed as special preimages for different canonical restriction functo rs (associated here also to Dynkin diagram inclusions). We will finally\, if time permits\, discuss potential applications of our results to the stu dy of cluster structures on Grothendieck rings. \n\nThis talk will take pl ace in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Baptiste Rognerud (Paris Cité) DTSTART;VALUE=DATE-TIME:20240603T120000Z DTEND;VALUE=DATE-TIME:20240603T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/168 DESCRIPTION:Title: The fractionally Calabi-Yau combinatorics of the Ta mari lattice\nby Baptiste Rognerud (Paris Cité) as part of Paris alge bra seminar\n\n\nAbstract\nA poset is said to be fractionally Calabi-Yau i f the bounded derived category of its incidence algebra over a field is fr actionally Calabi-Yau. In other words\, a power of the Serre functor is is omorphic to a shift. When going from a poset to its derived category\, one looses almost all the combinatorics of the poset. However in some favora ble cases\, part of the combinatorics is encoded in the Serre functor.\n\n In this talk\, I will present the combinatorics of the Serre functor of th e Tamari lattice. This leads to a more algebraic proof of its fractional C alabi-Yau property. It is also the first step toward a generalization to a larger family of posets. \n\nThis talk will take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Junyang Liu (USTC\, Hefei) DTSTART;VALUE=DATE-TIME:20240610T120000Z DTEND;VALUE=DATE-TIME:20240610T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/169 DESCRIPTION:Title: Singularity categories via McKay quivers with poten tial\nby Junyang Liu (USTC\, Hefei) as part of Paris algebra seminar\n \n\nAbstract\nIn 2018\, Kalck and Yang showed that the singularity categor ies associated with 3-dimensional Gorenstein quotient singularities are tr iangle equivalent (up to direct summands) to small cluster categories asso ciated with McKay quivers with potential. I introduce graded McKay quivers with potential and generalize Kalck-Yang's theorem to arbitrary dimension s. The singularity categories I consider occur as stable categories of cat egories of maximal Cohen-Macaulay modules. I refine my description of the singularity categories by showing that these categories of maximal Cohen-M acaulay modules are equivalent to Higgs categories in the sense of Wu. Mor eover\, I describe the singularity categories in the non-Gorenstein case. \n\nThis talk will take place on Zoom only.\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/16 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Gorsky (Vienna) DTSTART;VALUE=DATE-TIME:20240701T120000Z DTEND;VALUE=DATE-TIME:20240701T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/170 DESCRIPTION:Title: Deep points in cluster varieties\nby Mikhail Go rsky (Vienna) as part of Paris algebra seminar\n\n\nAbstract\nMany importa nt algebraic varieties\, such as open positroid strata in Grassmannians\, Richardson varieties\, or augmentation varieties of certain Legendrian lin ks\, are known to carry cluster structures. In particular\, each such vari ety is covered\, up to codimension 2\, by a collection of overlapping open tori. In this talk\, I will discuss the ``deep locus'' of a cluster varie ty\, that is\, the complement to the union of all cluster toric charts. I will explain a conjectural relation between the deep locus and the natural torus action compatible with the cluster structure. For many positroid st rata in Gr(2\,n) and Gr(3\,n)\, and for cluster varieties of types ADE\, t his relation is made precise: we show that the deep locus consists precise ly of the points with non-trivial stabilizer for this action. If time perm its\, I will explain how these results can be applied in the context of ho mological mirror symmetry and say a few words on the geometry of deep loci . The talk is based on joint work with Marco Castronovo\, José Simental\, and David Speyer (arXiv:2402.16970).\n\n\nThis talk will be on Zoom only. \n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/17 0/ END:VEVENT BEGIN:VEVENT SUMMARY:Isambard Goodbody (Glasgow) DTSTART;VALUE=DATE-TIME:20240930T120000Z DTEND;VALUE=DATE-TIME:20240930T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/171 DESCRIPTION:by Isambard Goodbody (Glasgow) as part of Paris algebra semina r\n\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/17 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilya Dumanskiy (MIT) DTSTART;VALUE=DATE-TIME:20241015T120000Z DTEND;VALUE=DATE-TIME:20241015T130000Z DTSTAMP;VALUE=DATE-TIME:20240910T210331Z UID:paris-algebra-seminar/172 DESCRIPTION:by Ilya Dumanskiy (MIT) as part of Paris algebra seminar\n\nAb stract: TBA\n LOCATION:https://master.researchseminars.org/talk/paris-algebra-seminar/17 2/ END:VEVENT END:VCALENDAR