BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Stephanie van Willigenburg (University of British Columbia)
DTSTART:20210618T150000Z
DTEND:20210618T160000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/1
DESCRIPTION:Title: The e-positivity of chromatic symmetric functions\nby Stephanie v
an Willigenburg (University of British Columbia) as part of Algebraic and
Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nThe
chromatic polynomial was generalized to the chromatic symmetric function
by Stanley in his seminal 1995 paper. This function is currently experienc
ing a flourishing renaissance\, in particular the study of the positivity
of chromatic symmetric functions when expanded into the basis of elementar
y symmetric functions\, that is\, e-positivity.\nIn this talk we approach
the question of e-positivity from various angles. Most pertinently we reso
lve the 1995 statement of Stanley that no known graph exists that is not c
ontractible to the claw\, and whose chromatic symmetric function is not e-
positive.\n\nThis is joint work with Soojin Cho\, Samantha Dahlberg\, Ange
le Foley and Adrian She\, and no prior knowledge is assumed.\n\nPlease not
e that this talk starts at 17:00 (GMT+2) instead of the usual time.
\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amy Pang (Hong Kong Baptist University)
DTSTART:20210625T130000Z
DTEND:20210625T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/2
DESCRIPTION:Title: Markov chains from linear operators and Hopf algebras\nby Amy Pan
g (Hong Kong Baptist University) as part of Algebraic and Combinatorial Pe
rspectives in the Mathematical Sciences\n\n\nAbstract\nIf you study a line
ar operator that expands positively in some basis\, then your results may
be applicable to a Markov chain\, whose transition probabilities are given
by the matrix of the operator. This is the idea behind the theory of rand
om walks on groups and monoids\, where the eigen-data of the operator info
rms the long-term behaviour of the chain. We point out a lesser-known adva
ntage of this framework: if the linear operator descends to a specific sub
quotient of its domain\, then the corresponding Markov chain admits a proj
ection / lumping. We apply this to a coproduct-then-product operator on Ho
pf algebras\, to explain Jason Fulman's observation regarding the RSK-shap
e under card-shuffling. I hope this talk will enable and inspire you to ex
plore new examples.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Dołęga (Polish Academy of Sciences)
DTSTART:20210702T130000Z
DTEND:20210702T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/3
DESCRIPTION:by Maciej Dołęga (Polish Academy of Sciences) as part of Alg
ebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbst
ract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Benedetti (Universidad de los Andes\, Bogotá)
DTSTART:20210709T130000Z
DTEND:20210709T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/4
DESCRIPTION:by Carolina Benedetti (Universidad de los Andes\, Bogotá) as
part of Algebraic and Combinatorial Perspectives in the Mathematical Scien
ces\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susama Agarwala (University of Hamburg)
DTSTART:20210903T130000Z
DTEND:20210903T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/5
DESCRIPTION:by Susama Agarwala (University of Hamburg) as part of Algebrai
c and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract:
TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Chapoton (CNRS\, Strasbourg)
DTSTART:20210910T130000Z
DTEND:20210910T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/6
DESCRIPTION:Title: Multiple zeta values and zinbiel algebras\nby Frédéric Chapoton
(CNRS\, Strasbourg) as part of Algebraic and Combinatorial Perspectives i
n the Mathematical Sciences\n\n\nAbstract\nWe will explain the constructio
n\, using the notion of Zinbiel algebra\, of some commutative subalgebras
$C_{u\,v}$ inside an algebra of formal iterated integrals. There is a quot
ient map from this algebra of formal iterated integrals to the algebra of
motivic multiple zeta values. Restricting this quotient map to the subalge
bras $C_{u\,v}$ gives a morphism of graded commutative algebras with the s
ame generating series. This is conjectured to be generically an isomorphis
m. When $u+v = 0$\, the image is instead a sub-algebra of the algebra of m
otivic multiple zeta values.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chaitanya Leena Subramaniam (Université Paris Diderot)
DTSTART:20210917T130000Z
DTEND:20210917T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/7
DESCRIPTION:Title: Dependent type theory and higher algebraic structures\nby Chaitan
ya Leena Subramaniam (Université Paris Diderot) as part of Algebraic and
Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn
classical universal algebra\, every family of algebraic structures (such a
s monoids\, groups\, rings\, modules\, small categories\, operads\, sheave
s) can be classified by a syntactic (algebraic or essentially algebraic) e
quational theory. A cornerstone of universal algebra is the equivalence be
tween algebraic theories and finitary monads on the category of sets\, due
to Lawvere\, B\\'enabou and Linton. Higher algebraic structures (such as
loop spaces\, E-k spaces\, infinity-categories\, infinity-operads and thei
r modules and algebras\, stacks\, spectra) are algebraic structures up to
homotopy in spaces ("spaces" = topological spaces\, simplicial sets or any
other model of homotopy types). It is a long-standing presupposition amon
g homotopy type theorists that the dependent types introduced by Martin-L\
\"of are particularly well-suited to providing syntactic theories and a un
iversal algebra for higher algebraic structures. In this talk\, we will se
e a (few) definition(s) of "dependently sorted/typed algebraic theory" and
describe a monad-theory equivalence strictly generalising that of Lawvere
-Bénabou-Linton. With respect to their Set-valued models\, dependently so
rted algebraic theories have the same expressive power as essentially alge
braic theories. However\, as we will see in this talk\, dependently sorted
algebraic theories have the advantage of having a good theory of models u
p-to-homotopy in spaces\, which generalises the theory of homotopy-models
of algebraic theories due to Schwede\, Badzioch\, Rezk and Bergner. We wil
l see that many familiar algebraic structures (such as n-categories\, omeg
a-categories\, coloured planar operads\, opetopic sets) are very naturally
seen to be models of dependently sorted algebraic theories. The crux of t
hese results is a correspondence between the dependent sorts/types of any
dependently sorted algebraic theory T\, and a certain "cellularity" underl
ying every algebraic structure described by T (i.e. every T-model). The go
al of this talk will be to explain this correspondence between type depend
ency and cellularity\, and why this cellularity marries well with homotopy
theory.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunnar Fløystad (University of Bergen)
DTSTART:20210924T130000Z
DTEND:20210924T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/8
DESCRIPTION:Title: Shift modules\, strongly stable ideals\, and their dualities\nby
Gunnar Fløystad (University of Bergen) as part of Algebraic and Combinato
rial Perspectives in the Mathematical Sciences\n\n\nAbstract\nPolynomial r
ings over a field $k$ are the prime objects in algebra. Ideals in polynomi
al rings are the prime objects relating algebra and geometry via the zero
set of the ideal.\n\nTo understand ideals in a polynomial ring\, a common
approach is to see what simpler ideals they degenerate to\, for instance w
hat monomial ideals. But what are the most degenerate ideals you can find?
Those that cannot be degenerated any further? These are the so-called Bor
el-fixed ideals\, or\, when the field k has characteristic zero\, the stro
ngly stable ideals. This class is for instance the essential tool for unde
rstanding numerical invariants of ideals in polynomial rings.\n\nWe enrich
the setting of strongly stable ideals by:\n\n1. Extending them to a categ
ory of modules\n\n2. Investigating the recently discovered duality on thes
e ideals\n\n3. Getting a new type of projective resolution of such ideals\
n\n4. Letting the ambient polynomial ring be infinite dimensional\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franz Herzog (The University of Edinburgh)
DTSTART:20211001T130000Z
DTEND:20211001T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/9
DESCRIPTION:Title: The Hopf algebra of IR divergences of Feynman graphs\nby Franz He
rzog (The University of Edinburgh) as part of Algebraic and Combinatorial
Perspectives in the Mathematical Sciences\n\n\nAbstract\nIt is by now very
well known that the structure of UV divergences Feynman Integrals\, and t
heir associated graphs\, can be described elegantly in a Hopf algebra orig
inally developed by Kreimer and Connes. Beyond UV divergences Feynman Inte
grals also suffer from IR\, long-distance\, divergences. I will present a
new Hopf-algebraic formulation which allows to simultaneously treat both t
he IR and the UV. Remarkably in this framework the IR and UV counterterm m
aps are inverse to each other on the group of characters of the Hopf algeb
ra.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Spirkl (University of Waterloo)
DTSTART:20211022T130000Z
DTEND:20211022T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/10
DESCRIPTION:Title: Modular relations for the Tutte symmetric function\nby Sophie Sp
irkl (University of Waterloo) as part of Algebraic and Combinatorial Persp
ectives in the Mathematical Sciences\n\n\nAbstract\nThe Tutte symmetric fu
nction XB generalizes both the Tutte polynomial and the chromatic symmetri
c function X. In this talk\, I'll discuss a modular relation for XB analog
ous to the Orellana-Scott relation for X\, general results for modular rel
ations for XB and X\, and applications.\nJoint work with Logan Crew.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerald Dunne (University of Connecticut)
DTSTART:20211029T130000Z
DTEND:20211029T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/11
DESCRIPTION:Title: Resurgent Trans-series in Hopf-Algebraic Dyson-Schwinger Equations\nby Gerald Dunne (University of Connecticut) as part of Algebraic and C
ombinatorial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bérénice Delcroix-Oger (Université de Paris)
DTSTART:20211217T140000Z
DTEND:20211217T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/12
DESCRIPTION:by Bérénice Delcroix-Oger (Université de Paris) as part of
Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nA
bstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Gilliers (University of Toulouse)
DTSTART:20211008T130000Z
DTEND:20211008T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/13
DESCRIPTION:Title: Binary trees\, operads and Dykema’s T-transform in Free Probabilit
y\nby Nicolas Gilliers (University of Toulouse) as part of Algebraic a
nd Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\n
In this talk\, we shall discuss an operadic perspective on K. Dykema’s t
wisted factorization formula for the operator-valued T-transform in free p
robability. To begin with\, we introduce in the general setting of an oper
ad with multiplication two group products on formal series of operators\,
besides the one introduced by F. Chapoton. We explain how those products r
elate by means of certain transformation\, that we call (abstract) T-trans
form\, borrowing terminology from free probability. Specializing in the en
domorphism operad gives a new perspective on the twisted factorization of
the T-transform and to multiplicative free convolution. We will discuss co
nnections to the work of A. Frabetti and C. Brouder by specializing our co
nstruction to the duoidal and dendriform operads.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannic Vargas (University of Potsdam)
DTSTART:20211015T130000Z
DTEND:20211015T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/14
DESCRIPTION:Title: Monomial bases for combinatorial Hopf algebras\nby Yannic Vargas
(University of Potsdam) as part of Algebraic and Combinatorial Perspectiv
es in the Mathematical Sciences\n\n\nAbstract\nThe algebraic structure of
a Hopf algebra can often be understood in terms of a poset on the underlyi
ng family of combinatorial objects indexing a basis. For example\, the Hop
f algebra of quasisymmetric functions is generated (as a vector space) by
compositions and admits a fundamental (F) basis and a monomial (M) basis\,
related by the refinement poset on compositions. Analogous bases can be c
onsidered for other Hopf algebras\, with similar properties to the F basis
\, e.g. a product described by some notion of shuffle\, and a coproduct fo
llowing some notion of deconcatenation. We give axioms for how these gener
alised shuffles and deconcatentations should interact with the underlying
poset so that a monomial-like basis can be analogously constructed\, gener
alising the approach of Aguiar and Sottile. We also find explicit positive
formulas for the multiplication on monomial basis and a cancellation-free
and grouping-free formula for the antipode of monomial elements. We apply
these results on classical and new Hopf algebras\, related by tree-like s
tructures.\nThis is based on "Hopf algebras of parking functions and decor
ated planar trees"\, a joint work with Nantel Bergeron\, Rafael Gonzalez D
'Leon\, Amy Pang and Shu Xiao Li.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonard Schmitz (University of Greifswald)
DTSTART:20230120T140000Z
DTEND:20230120T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/15
DESCRIPTION:Title: Two-parameter sums signatures and corresponding quasisymmetric funct
ions\nby Leonard Schmitz (University of Greifswald) as part of Algebra
ic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract
: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaiung Jun (SUNY at New Paltz)
DTSTART:20230317T140000Z
DTEND:20230317T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/16
DESCRIPTION:Title: On the Hopf algebra of multi-complexes\nby Jaiung Jun (SUNY at N
ew Paltz) as part of Algebraic and Combinatorial Perspectives in the Mathe
matical Sciences\n\n\nAbstract\nHopf algebras appear naturally in combinat
orics in the following way: For a given class of combinatorial objects (su
ch as graphs or matroids)\, basic operations (such as assembly and disasse
mbly operations) often can be encoded in the algebraic structure of a Hopf
algebra. One then hopes to use algebraic identities of a Hopf algebra to
return to combinatorial identities of combinatorial objects of interest. I
n this talk\, I will introduce a general class of combinatorial objects\,
which we call multi-complexes. They simultaneously generalize graphs\, hyp
ergraphs and simplicial and delta complexes. I will describe the structure
of the Hopf algebra of multi-complexes by finding an explicit basis of th
e space of primitives. This is joint work with Miodrag Iovanov.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annika Burmester (Bielefeld University)
DTSTART:20230331T130000Z
DTEND:20230331T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/17
DESCRIPTION:Title: Post-Lie algebras related to multiple (q-)zeta values\nby Annika
Burmester (Bielefeld University) as part of Algebraic and Combinatorial P
erspectives in the Mathematical Sciences\n\n\nAbstract\nMultiple zeta valu
es became of more interest over the last 25 years due to their appearance
in various fields of mathematics and also physics. First\, we will describ
e their algebraic structure in terms of Hoffman’s quasi-shuffle algebras
\, which are certain deformations of the usual shuffle product. Following
Racinet this allows to relate a post-Lie algebra to the multiple zeta valu
es\, the double shuffle Lie algebra equipped with the Ihara bracket\, whic
h gives a new insight into the algebraic structure of multiple zeta values
. We are interested in an analog approach for multiple q-zeta values\, whi
ch are certain q-series degenerating to multiple zeta values for the limit
q to 1. In particular\, we will explain some results towards a post-Lie a
lgebra related to multiple q-zeta values.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karine Beauchard (ENS Rennes)
DTSTART:20230414T130000Z
DTEND:20230414T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/18
DESCRIPTION:Title: On expansions for nonlinear systems\, error estimates and convergenc
e issues\nby Karine Beauchard (ENS Rennes) as part of Algebraic and Co
mbinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nExpli
cit formulas expressing the solution to non-autonomous differential equati
ons are of great importance in many application domains such as control th
eory or numerical operator splitting. In particular\, intrinsic formulas a
llowing to decouple time-dependent features from geometry-dependent featur
es of the solution have been extensively studied.\nFirst\, we give a didac
tic review of classical expansions for formal linear differential equation
s\, including the celebrated Magnus expansion (associated with coordinates
of the first kind) and Sussmann’s infinite product expansion (associate
d with coordinates of the second kind). Inspired by quantum mechanics\, we
introduce a new mixed expansion\, designed to isolate the role of a time-
invariant drift from the role of a time-varying perturbation.\nSecond\, in
the context of nonlinear ordinary differential equations driven by regula
r vector fields\, we give rigorous proofs of error estimates between the e
xact solution and finite approximations of the formal expansions. In parti
cular\, we derive new estimates focusing on the role of time-varying pertu
rbations.\nThird\, we investigate the local convergence of these expansion
s. In particular\, we exhibit arbitrarily small analytic vector fields for
which the convergence of the Magnus expansion fails\, even in very weak s
enses.\nEventually\, we derive approximate direct intrinsic representation
s for the state\, particularly well designed for applications in control t
heory.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darij Grinberg
DTSTART:20230428T130000Z
DTEND:20230428T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/19
DESCRIPTION:by Darij Grinberg as part of Algebraic and Combinatorial Persp
ectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunnar Fløystad
DTSTART:20230512T130000Z
DTEND:20230512T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/20
DESCRIPTION:by Gunnar Fløystad as part of Algebraic and Combinatorial Per
spectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Meroni
DTSTART:20230526T130000Z
DTEND:20230526T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/21
DESCRIPTION:Title: Path signatures in convex geometry\nby Chiara Meroni as part of
Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\
nAbstract\nHow can one compute the volume of the convex hull of a curve? I
will try to answer this question\, for special families of curves. This i
s a joint work with Carlos Améndola and Darrick Lee. We generalise the cl
ass of curves for which a certain integral formula works\, using the techn
ique of signatures. I will then give a geometric interpretation of this vo
lume formula in terms of lengths and areas\, and conclude with examples an
d an open conjecture.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilie Purvine
DTSTART:20230609T140000Z
DTEND:20230609T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/22
DESCRIPTION:Title: Applied Topology for Discrete Structures\nby Emilie Purvine as p
art of Algebraic and Combinatorial Perspectives in the Mathematical Scienc
es\n\n\nAbstract\nDiscrete structures have a long history of use in applie
d mathematics. Graphs and hypergraphs provide models of social networks\,
biological systems\, academic collaborations\, and much more. Network scie
nce\, and more recently hypernetwork science\, have been used to great eff
ect in analyzing these types of discrete structures. Separately\, the fiel
d of applied topology has gathered many successes through the development
of persistent homology\, mapper\, sheaves\, and other concepts. Recent wor
k by our group has focused on the convergence of these two areas\, develop
ing and applying topological concepts to study discrete structures that mo
del real data. This talk will survey our body of work in this area showing
our work in both the theoretical and applied spaces. Theory topics will i
nclude an introduction to hypernetwork science and its relation to traditi
onal network science\, topological interpretations of graphs and hypergrap
hs\, and dynamics of topology and network structures. I will show examples
of how we are applying each of these concepts to real data sets.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Verri (Universität Greifswald)
DTSTART:20230623T130000Z
DTEND:20230623T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/23
DESCRIPTION:Title: Conjoined permutation patterns\nby Emanuele Verri (Universität
Greifswald) as part of Algebraic and Combinatorial Perspectives in the Mat
hematical Sciences\n\n\nAbstract\nSome time ago\, Bandt introduced the con
cept of "permutation entropy" which proved very effective in the analysis
of time series.\nThis index is based on certain permutation patterns.\nPer
mutation patterns play indeed a very central role in many areas of discret
e mathematics.\nMore recently\, in algebraic combinatorics\, Vargas introd
uced the superinfiltration Hopf algebra whose operations behave well with
respect to occurrences of permutation patterns.\nInspired by both these wo
rks\, we introduce a new Hopf algebra which also includes the patterns use
d by Bandt.\nIts algebraic operations behave well with respect to occurren
ces of permutation patterns where is also specified whether values are con
secutive or arbitrarily far apart.\nTo encode whether two values are conse
cutive\, we use interval partitions of finite subsets of positive integers
and also introduce a new Hopf algebra on interval partitions.\nThis is jo
int work with Joscha Diehl.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20230707T130000Z
DTEND:20230707T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/24
DESCRIPTION:by TBA as part of Algebraic and Combinatorial Perspectives in
the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Olson-Harris (University of Waterloo)
DTSTART:20230918T130000Z
DTEND:20230918T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/25
DESCRIPTION:by Nick Olson-Harris (University of Waterloo) as part of Algeb
raic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstra
ct: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasia Rejzner (University of York)
DTSTART:20230929T130000Z
DTEND:20230929T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/26
DESCRIPTION:Title: Perturbative algebraic quantum field theory (introduction and exampl
es)\nby Kasia Rejzner (University of York) as part of Algebraic and Co
mbinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn th
is talk I will introduce the framework perturbative algebraic quantum fiel
d theory. It allows one to combine the method of Epstein-Glaser renormalis
ation with the idea of BV quantization\, commonly applied to quantization
of gauge theories. It straightforwardly generalizes to theories on a large
class of Lorentzian manifolds. The same formalism can also be applied whe
n one replaces the manifold with a finite collection of points\, equipped
with a partial order relation (modelling the causal order).\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Olson-Harris
DTSTART:20231013T130000Z
DTEND:20231013T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/27
DESCRIPTION:by Nick Olson-Harris as part of Algebraic and Combinatorial Pe
rspectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro)
DTSTART:20231027T130000Z
DTEND:20231027T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/28
DESCRIPTION:Title: About local symplectic groupoids and applications\nby Alejandro
Cabrera (Universidade Federal do Rio de Janeiro) as part of Algebraic and
Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn
this talk\, we will review the notion of local symplectic groupoid and its
relation to Poisson geometry. We then summarize some recent results invol
ving explicit constructions and their relation to quantization. Finally\,
we will comment on applications to discretization of hamiltonian flows on
Poisson manifolds.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette
DTSTART:20231117T140000Z
DTEND:20231117T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/30
DESCRIPTION:by Bruno Vallette as part of Algebraic and Combinatorial Persp
ectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matilde Marcolli
DTSTART:20231201T140000Z
DTEND:20231201T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/31
DESCRIPTION:by Matilde Marcolli as part of Algebraic and Combinatorial Per
spectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Pechenik (University of Waterloo)
DTSTART:20231215T140000Z
DTEND:20231215T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/32
DESCRIPTION:Title: Quasisymmetric Schubert calculus\nby Oliver Pechenik (University
of Waterloo) as part of Algebraic and Combinatorial Perspectives in the M
athematical Sciences\n\n\nAbstract\nWe introduce projective schemes that a
re analogues of the James reduced product construction from homotopy theor
y and begin to develop a Schubert calculus for such spaces. This machinery
yields K-theoretic and T-equivariant analogues of classic quasisymmetric
function theory. Based on joint works with Matt Satriano.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Shiebler (Abnormal Security)
DTSTART:20240126T140000Z
DTEND:20240126T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/33
DESCRIPTION:Title: Learning with Kan Extensions\nby Dan Shiebler (Abnormal Security
) as part of Algebraic and Combinatorial Perspectives in the Mathematical
Sciences\n\n\nAbstract\nA common problem in machine learning is "use this
function defined over this small set to generate predictions over that lar
ger set." Extrapolation\, interpolation\, statistical inference and foreca
sting all reduce to this problem. The Kan extension is a powerful tool in
category theory that generalizes this notion. In this work we explore appl
ications of the Kan extension to machine learning problems. We begin by de
riving a simple classification algorithm as a Kan extension and experiment
ing with this algorithm on real data. Next\, we use the Kan extension to d
erive a procedure for learning clustering algorithms from labels and explo
re the performance of this procedure on real data.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolas Tapia (Weierstrass Institute)
DTSTART:20240209T140000Z
DTEND:20240209T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/34
DESCRIPTION:Title: Branched Itô Formula and natural Itô-Stratonovich isomorphism\
nby Nikolas Tapia (Weierstrass Institute) as part of Algebraic and Combina
torial Perspectives in the Mathematical Sciences\n\n\nAbstract\nBranched r
ough paths define integration theories that may fail to satisfy the integr
ation by parts identity. The projection of the Connes-Kreimer Hopf algebra
(\\(\\mathcal{H}_{\\mathrm{CK}}\\)) onto its primitive elements defined b
y Broadhurst-Kreimer and Foissy\, allows us to view \\(\\mathcal{H}_{\\mat
hrm{CK}}\\) as a commutative \\(\\mathbf{B}_\\infty\\)-algebra and thus to
write an explicit change-of-variable formula for solutions to rough diffe
rential equations (RDEs)\, which restricts to the well-known Itô formula
for semimartingales. When compared with Kelly’s approach using bracket e
xtensions\, this formula has the advantage of only depending on internal s
tructure. We proceed to define an isomorphism between \\(\\mathcal{H}_{\\m
athrm{CK}}\\) and \\(\\operatorname{Sh}(\\mathcal{P})\\) (the shuffle alge
bra over primitives)\, which we compare with the previous constructions of
Hairer-Kelly and Boedihardjo-Chevyrev: while all three allow one to write
branched RDEs as RDEs driven by geometric rough paths taking values in a
larger space\, the key feature of our isomorphism is that it is natural wh
en \\(\\mathcal{H}_{\\mathrm{CK}}\\) and \\(\\operatorname{Sh}(\\mathcal{P
})\\) are viewed as covariant functors \\(\\mathsf{Vec}\\to\\mathsf{Hopf}\
\). Our natural isomorphism extends Hoffman’s exponential for the quasi
shuffle algebra\, and in particular the usual Itô-Stratonovich correction
formula for semimartingales. Special emphasis is placed on the 1-dimensio
nal case\, in which certain rough path terms can be expressed as polynomia
ls in the trace path indexed by \\(\\mathcal{P}\\)\, which for semimarting
ales restrict to the well-known Kailath-Segall polynomials.\n\nThis talk i
s based on joint work with E. Ferrucci and C. Bellingeri.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Kern (TU Berlin)
DTSTART:20240301T140000Z
DTEND:20240301T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/35
DESCRIPTION:Title: Rough Flow techniques on manifolds\nby Hannes Kern (TU Berlin) a
s part of Algebraic and Combinatorial Perspectives in the Mathematical Sci
ences\n\n\nAbstract\nIn 2020\, Armstrong et al managed to explicitly write
down Davie’s formula of the solution of a non-geometric RDE on a manifo
ld for the level N = 2. In this talk\, we introduce a new notion\, called
pseudo bialgebra map\, which allows us to construct similar expansions for
higher level rough pahs living in general Hopf algebras. To do this\, we
prove a local version of Bailleul’s sewing lemma for flows. Finally\, we
go over previous results and show that they do give rise to pseudo bialge
bra maps. Based on joint work with Terry Lyons.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruggero Bandiera (Sapienza Università di Roma)
DTSTART:20240315T140000Z
DTEND:20240315T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/36
DESCRIPTION:Title: Cumulants\, Koszul brackets and homological perturbation theory for
commutative BVoo and IBLoo algebras\nby Ruggero Bandiera (Sapienza Uni
versità di Roma) as part of Algebraic and Combinatorial Perspectives in t
he Mathematical Sciences\n\n\nAbstract\nn the first part of this talk we s
hall review the classical homotopy transfer theorem in the context of Aoo
and Loo algebras. We shall explain how the usual proof of this result for
Aoo algebras\, based on the tensor trick and the homological perturbation
lemma\, can be adapted to Loo algebras using a symmetrized version of the
tensor trick. In the course of the discussion we shall review the construc
tion of cumulants and Koszul brackets (as well as their coalgebraic analog
s): these are graded symmetric multilinear maps associated respectively to
a morphism of graded commutative algebras $f\\colon A \\to B$ or to an en
domorphism $d\\colon A \n\\to A$\, measuring the deviation of f from being
an algebra morphism in the first case\, and the deviation of d from being
an algebra derivation in the second case. A key technical lemma will be t
hat under certain assumptions on the involved contraction\, these are comp
atible with homotopy transfer in an appropriate sense. In the second part
of the talk we shall review commutative BVoo algebra in the sense of Kravc
henko: as an application of our previous discussion we shall introduce a n
ew definition of morphisms between these objects in terms of cumulants. Mo
reover\, we shall explain how to use homological perturbation theory to ge
t a homotopy transfer theorem for commutative BVoo algebras\, under certai
n assumptions on the involved contraction. Finally\, IBLoo algebras\, that
is\, commutative BVoo algebras whose underlying algebra is free\, are kno
wn to be a model for involutive Lie bialgebras up to coherent homotopies\,
and have recently found several applications in string topology and sympl
ectic field theory. \nAs an application of our results\, we shall explain
how to obtain a homotopy transfer theorem for IBLoo algebras via the symme
trized tensor trick and the homological perturbation lemma.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Joswig (TU Berlin)
DTSTART:20240223T140000Z
DTEND:20240223T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/37
DESCRIPTION:Title: Quantum automorphisms of matroids\nby Michael Joswig (TU Berlin)
as part of Algebraic and Combinatorial Perspectives in the Mathematical S
ciences\n\n\nAbstract\nMotivated by the vast literature of quantum automor
phism groups of graphs\, we define and study quantum automorphism groups o
f matroids. A key feature of quantum groups is that there are many quantiz
ations of a classical group\, and this phenomenon manifests in the cryptom
orphic characterizations of matroids. Our primary goals are to understand\
, using theoretical and computational techniques\, the relationship betwee
n these quantum groups and to find when these quantum groups exhibit quant
um symmetry. Finally\, we prove a matroidal analog of Lovász's theorem ch
aracterizing graph isomorphisms in terms of homomorphism counts.\n\nJoint
work with Daniel Corey\, Julien Schanz\, Marcel Wack\, and Moritz Weber.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Turner (Imperial College London)
DTSTART:20240405T130000Z
DTEND:20240405T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/38
DESCRIPTION:Title: Free probability\, path developments and signature kernels as univer
sal scaling limits\nby William Turner (Imperial College London) as par
t of Algebraic and Combinatorial Perspectives in the Mathematical Sciences
\n\n\nAbstract\nScaling limits of random developments of a path into a mat
rix Lie Group have recently been used to construct signature-based kernels
on path space\, while mitigating some of the dimensionality challenges th
at come with using signatures directly. Muça Cirone et al. have establish
ed a connection between the scaling limit of general linear group developm
ents with Gaussian vector fields and the ordinary signature kernel\, while
Lou et al. utilised unitary group developments and previous work of Chevy
rev and Lyons to construct a path characteristic function distance. By lev
eraging the tools of random matrix theory and free probability theory\, we
are able to provide a unified treatment of the limits in both settings un
der general assumptions on the vector fields. For unitary developments\, w
e show that the limiting kernel is given by the contraction of a signature
against the monomials of freely independent semicircular random variables
. Using the Schwinger-Dyson equations\, we show that this kernel can be ob
tained by solving a novel quadratic functional equation.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helena Bergold (Freie Universität Berlin)
DTSTART:20240419T130000Z
DTEND:20240419T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/39
DESCRIPTION:Title: An Extension Theorem for Signotopes\nby Helena Bergold (Freie Un
iversität Berlin) as part of Algebraic and Combinatorial Perspectives in
the Mathematical Sciences\n\n\nAbstract\nIn 1926\, Levi showed that\, for
every pseudoline arrangement $A$ and two\npoints in the plane\, $A$ can be
extended by a pseudoline which contains\nthe two prescribed points. Later
extendability was studied for\narrangements of pseudohyperplanes in highe
r dimensions. While the\nextendability of an arrangement of proper hyperpl
anes in R^d with a\nhyperplane containing $d$ prescribed points is trivial
\, Richter-Gebert\nfound an arrangement of pseudoplanes in R^3 which canno
t be extended\nwith a pseudoplane containing two particular prescribed poi
nts.\nIn this talk\, we investigate the extendability of signotopes\, whic
h are\na combinatorial structure encoding a rich subclass of pseudohyperpl
ane\narrangements. We show that signotopes of odd rank are extendable in t
he\nsense that for two prescribed crossing points we can add an element\nc
ontaining them.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrien Laurent
DTSTART:20240503T130000Z
DTEND:20240503T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/40
DESCRIPTION:Title: On the geometric and algebraic properties of stochastic backward err
or analysis\nby Adrien Laurent as part of Algebraic and Combinatorial
Perspectives in the Mathematical Sciences\n\n\nAbstract\nThe exotic aromat
ic extension of Butcher series allowed the creation and study of integrato
rs for the high-order sampling of the invariant measure of ergodic stochas
tic differential equations. In particular\, the concept of backward error
analysis\, a key concept in geometric numerical integration\, seemed to ge
neralise in a certain sense for the study of stochastic dynamics using exo
tic aromatic B-series\, though there was no general result beyond order 3.
In this talk\, we will detail the concept of backward error analysis\, qu
ickly present recent results on the Hopf algebra structures related to the
composition and substitution laws of exotic aromatic series\, and see tha
t stochastic backward error analysis writes naturally and at any order wit
h exotic aromatic B-series. Then\, we shall show that the exotic aromatic
formalism is precisely the right formalism for the formulation of backward
error analysis\, thanks to a universal geometric property of orthogonal e
quivariance. This is joint work with Eugen Bronasco (University of Geneva)
and Hans Munthe-Kaas (University of Bergen and University of Tromsø).\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cyril Banderier
DTSTART:20240517T130000Z
DTEND:20240517T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/41
DESCRIPTION:Title: From geometry to generating functions: rectangulations and permutati
ons\nby Cyril Banderier as part of Algebraic and Combinatorial Perspec
tives in the Mathematical Sciences\n\n\nAbstract\nA rectangulation of size
n is a tiling of a rectangle by n rectangles such that no four rectangles
meet in a point. In the literature\, rectangulations are also called floo
rplans or rectangular dissections. In this talk\, we will analyse several
classes of pattern-avoiding rectangulations which lead to surprisingly nic
e enumerative results and new bijective links with pattern-avoiding permut
ations. We prove that their generating functions are algebraic\, and confi
rm several conjectures by Merino and Mütze. We also analyse a new class
of rectangulations\, called whirls: they are related to Catalan numbers\,
but no simple proof of it is known! We prove this fact using a generating
tree. This leads to an intricate functional equation\, for which the metho
d of resolution has its own interest.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Bellingeri
DTSTART:20240531T130000Z
DTEND:20240531T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/42
DESCRIPTION:Title: The Euler-Maclaurin formula and generalised iterated integrals\n
by Carlo Bellingeri as part of Algebraic and Combinatorial Perspectives in
the Mathematical Sciences\n\n\nAbstract\nConsidered one of the key identi
ties in classical analysis\, the Euler-McLaurin formula is one of the stan
dard tools for relating sums and integrals\, with remarkable applications
in many areas of mathematics\, although it is little used in stochastic an
alysis. In this talk\, we will show how\, by introducing new variants of t
he iterated integrals of a path and a simple variational problem\, we can
generalise this identity in the context of Riemann Stieltjes integration.
Joint work with Sylvie Paycha (Potsdam) and Peter Friz (TU Berlin and WIAS
)\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Fritz
DTSTART:20240607T130000Z
DTEND:20240607T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/43
DESCRIPTION:Title: Self-distributive structures in physics\nby Tobias Fritz as part
of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\
n\n\nAbstract\nIn all of our current physical theories\, it is a central f
eature that observables generate 1-parameter groups of transformations. Fo
r example\, a Hamiltonian generates time translations\, while the angular
momentum observable generates rotations. In this talk\, I will explain how
this property is captured algebraically by the new notion of Lie quandle.
The central ingredient is a version of the self-distributivity equation $
x\\rhd(y\\rhd z)=(x\\rhd y)\\rhd(x\\rhd z)$. I will argue that Lie quandle
s can be thought of as nonlinear generalizations of Lie algebras. It is in
triguing that not only the observables of physical theories form a Lie qua
ndle\; the same is true for the (mixed) states\, where the Lie quandle str
ucture is given by the formation of probabilistic mixtures.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christine Vespa (Université d'Aix-Marseille)
DTSTART:20240906T130000Z
DTEND:20240906T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/44
DESCRIPTION:Title: Wheeled PROP structure on stable cohomology\nby Christine Vespa
(Université d'Aix-Marseille) as part of Algebraic and Combinatorial Persp
ectives in the Mathematical Sciences\n\n\nAbstract\nWheeled PROPs\, introd
uced by Markl\, Merkulov and Shadrin are PROPs equipped with extra structu
res which can treat traces. In this talk\, after explaining the notions of
PROPs and wheeled PROPs\, I will describe a wheeled PROP structure on sta
ble cohomology of automorphism groups of free groups with some particular
coefficients. I will explain how cohomology classes constructed previously
by Kawazumi can be interpreted using this wheeled PROP structure and I wi
ll construct a morphism of wheeled PROPs from a PROP given in terms of fun
ctor homology and the wheeled PROP evoked previously. This is joint work w
ith Nariya Kawazumi.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin
DTSTART:20240920T130000Z
DTEND:20240920T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/45
DESCRIPTION:Title: What is a skew brace?\nby Leandro Vendramin as part of Algebraic
and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstract
\nThe talk is an introduction to the theory of skew braces and their appli
cation to the\nstudy of combinatorial solutions of the Yang-Baxter equatio
n.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Dudzik
DTSTART:20240628T130000Z
DTEND:20240628T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/46
DESCRIPTION:by Andrew Dudzik as part of Algebraic and Combinatorial Perspe
ctives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Laubie (IRMA Strasbourg)
DTSTART:20250131T140000Z
DTEND:20250131T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/47
DESCRIPTION:Title: Volume preservation of Butcher series methods from the operadic view
point\nby Paul Laubie (IRMA Strasbourg) as part of Algebraic and Combi
natorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nAfter a
quick introduction on Butcher series methods\, we recall the theorem of Is
erles-Quispel-Tse/Chartier-Murua on the nonexistence of volume preserving
Butcher series methods. We will then give some algebraic and combinatorial
recollections on operads\, and introduce the operads and the techniques a
ppearing in the new proof of this theorem. If time permits\, we will expla
in how the operadic viewpoint also allows us to recover the full classific
ation of volume preserving aromatic Butcher series methods\, which was fir
st computed by Laurent\, McLachlan\, Munthe-Kaas\, and Verdier.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunnar Fløystad (University of Bergen)
DTSTART:20250214T140000Z
DTEND:20250214T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/48
DESCRIPTION:Title: Submodular functions\, generalized permutahedra\, conforming preorde
rs\, and cointeracting bialgebras\nby Gunnar Fløystad (University of
Bergen) as part of Algebraic and Combinatorial Perspectives in the Mathema
tical Sciences\n\n\nAbstract\nGeneralized permutahedra (GP) is a central c
lass of polyhedra with surprisingly many connections to various areas. Exa
mples are matroid polytopes and and \npolymatroids. GP are also equivalent
to submodular functions\, an\nimportant class in optimization and economi
cs.\n\nTo a submodular function we:\nDefine a class of preorders\, conform
ing preorders\nWe show the faces of a GP are in bijection with the conform
ing preorders.\nThe face poset structure of the GP induces two order relat
ions on conforming preorders\, subdivision and contraction\, and we invest
igate their properties.\nThere is Hopf monoid of submodular functions. We
show it has a bimonoid of modular functions cointeracting in a non-standar
d way. By recent theory of L.Foissy this associates a canonical polynomial
to any submodular function.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khalef Yaddaden (Nagoya University)
DTSTART:20250314T140000Z
DTEND:20250314T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/49
DESCRIPTION:Title: Schemes of double shuffle and distribution relations among cyclotomi
c multiple zeta values\nby Khalef Yaddaden (Nagoya University) as part
of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\
n\n\nAbstract\nWe are interested in two formal approaches reflecting the c
ombinatorial properties of double shuffle relations between cyclotomic mul
tiple zeta values of level \\(N \\ge 1\\). The first approach\, introduced
by Racinet\, considers cyclotomic multiple zeta values from the perspecti
ve of the Drinfeld associator and provides a description based on Hopf alg
ebra coproducts\, which he encodes in a scheme DMR(N). The second\, studie
d by Hoffmann\, Ihara-Kaneko-Zagier (\\(N=1\\))\, Arakawa-Kaneko and Zhao
(\\(N \\ge 1\\))\, describes these relations through algebra products that
we encode in a scheme EDS(N). When \\(N > 1\\)\, the cyclotomic multiple
zeta values of level N also satisfy distribution relations that Racinet in
corporates into a subscheme DMRD(N) of DMR(N). In this presentation\, we e
stablish an isomorphism between the schemes DMR(N) and EDS(N)\, then intro
duce a subscheme EDSD(N) of EDS(N) that we identify with DMRD(N). This ide
ntification enables us to prove a conjecture of Zhao stating that the weig
ht 2 distribution relations are a consequence of double shuffle relations
as well as weight 1 and depth 2 distribution relations (this talk is based
on a joint work with Henrik Bachmann).\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kim Jung-Wook (Albert Einstein Institute)
DTSTART:20250425T130000Z
DTEND:20250425T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/50
DESCRIPTION:Title: Algebra of graphs for scattering dynamics\nby Kim Jung-Wook (Alb
ert Einstein Institute) as part of Algebraic and Combinatorial Perspective
s in the Mathematical Sciences\n\n\nAbstract\nFeynman diagrams are an icon
ic instance of diagrammatic tools in theoretical physics\, which were deve
loped for describing quantum scattering dynamics of particles in quantum f
ield theory. With a small modification to diagrammatic rules\, the Feynman
diagrams can be repurposed to describe classical scattering dynamics\, wh
ere rooted tree graphs are given a special role of computing the impulse (
momentum change from scattering). I will explain how repackaging the class
ical scattering dynamics as a symmetry transformation (symplectic transfor
mation) leads to the Poisson algebra of directed tree graphs\, the Magnus
series\, and the Hopf algebra of graphs by Calaque\, Ebrahimi-Fard\, and M
anchon. This talk is based on arXiv:2410.22988 [hep-th]\, a work in collab
oration with Joon-Hwi Kim\, Sungsoo Kim\, and Sangmin Lee.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Patras (Université Côte d'Azur)
DTSTART:20250411T130000Z
DTEND:20250411T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/51
DESCRIPTION:Title: Matrix symmetric and quasi-symmetric functions\nby Frédéric Pa
tras (Université Côte d'Azur) as part of Algebraic and Combinatorial Per
spectives in the Mathematical Sciences\n\n\nAbstract\nA fundamental result
by L. Solomon states that formulas for the computation of tensor products
of symmetric group representations can be lifted to the corresponding (So
lomon’s) descent algebra\, a subalgebra of the group algebra with a very
rich structure. Motivated by the structure of the product formula in thes
e algebras and by other results and ideas in the field\, we introduce and
investigate a two dimensional analog based on packed integer matrices that
inherits most of their fundamental properties. One of the structures we i
ntroduce identifies with a bialgebra recently introduced by J. Diehl and L
. Schmitz to define a two dimensional generalisation of Chen’s iterated
integrals signatures. J.w. with L. Foissy and C. Malvenuto.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loïc Foissy
DTSTART:20250509T130000Z
DTEND:20250509T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/52
DESCRIPTION:Title: Double bialgebra of noncrossing partitions\nby Loïc Foissy as p
art of Algebraic and Combinatorial Perspectives in the Mathematical Scienc
es\n\n\nAbstract\nA double bialgebra is a family $(A\,m\,\\Delta\,\\delta)
$ such that both $(A\,m\,\\Delta)$ and $(A\,m\,\\delta)$ are bialgebras\,
with the extra condition that seeing $\\delta$ as a right coaction on itse
lf\, $m$ and $\\Delta$ are right comodules morphism over $(A\,m\,\\delta)$
. A classical example is given by the polynomial algebra $\\mathbb{C}[X]$\
, with its two classical coproducts. In this talk\, we will present a doub
le bialgebra structure on the symmetric algebra generated by noncrossing p
artitions. The first coproduct is given by the separations of the blocks o
f the partitions\, with respect to the entanglement\, and the second one b
y fusions of blocks. This structure implies that there exists a unique pol
ynomial invariant on noncrossing partitions which respects both coproducts
: we will give some elements on this invariant\, and applications to the a
ntipode of noncrossing partitions.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentine Soto
DTSTART:20250523T130000Z
DTEND:20250523T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/53
DESCRIPTION:Title: Generalized Kauer moves and derived equivalences of skew Brauer grap
h algebras\nby Valentine Soto as part of Algebraic and Combinatorial P
erspectives in the Mathematical Sciences\n\n\nAbstract\nBrauer graph algeb
ras are finite dimensional algebras constructed from the combinatorial dat
a of a graph called a Brauer graph. Kauer proved that derived equivalences
of Brauer graph algebras can be obtained from the move of one edge in the
corresponding Brauer graph. Moreover\, this derived equivalence is entire
ly described thanks to a tilting object which can be interpreted in terms
of silting mutation. In this talk\, I will be interested in skew Brauer gr
aph algebras which generalize the class of Brauer graph algebras. These al
gebras are constructed from the combinatorial data of a Brauer graph where
some edges might be "degenerate". I will explain how Kauer's results can
be generalized for the move of multiple edges and to the case of skew Brau
er graph algebras.\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tal Gottesman (Ruhr-Universität Bochum)
DTSTART:20250606T130000Z
DTEND:20250606T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/54
DESCRIPTION:Title: Fractional Calabi-Yau lattices\nby Tal Gottesman (Ruhr-Universit
ät Bochum) as part of Algebraic and Combinatorial Perspectives in the Mat
hematical Sciences\n\n\nAbstract\nF. Chapoton made public in 2023 an intri
guing conjecture linking combinatorial formulas\, symplectic geometry\, an
d representation theory of fractional Calabi-Yau posets. After exposing r
ecent progress around this conjecture\, I shall present the fractional Cal
abi-Yau property for lattices and how to prove it. If time permits\, I'll
consider the poset of plane partitions\, for which the conjecture remains
open\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcel Wack (TU Berlin)
DTSTART:20251010T130000Z
DTEND:20251010T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/55
DESCRIPTION:by Marcel Wack (TU Berlin) as part of Algebraic and Combinator
ial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/ACPMS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulf Kühn (Universität Hamburg)
DTSTART:20250620T130000Z
DTEND:20250620T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/56
DESCRIPTION:Title: Interesting coproducts through post-Lie algebras\nby Ulf Kühn (
Universität Hamburg) as part of Algebraic and Combinatorial Perspectives
in the Mathematical Sciences\n\n\nAbstract\nThis talk reports on joint wor
k with Annika Burmester\, https://arxiv.org/abs/2504.19661 . We study post
-Lie structures on free Lie algebras\, the Grossman-Larson product on thei
r enveloping algebras\, and provide an abstract formula for its dual copro
duct. This might be of interest for the general theory of post-Hopf algebr
as. Using a magmatic approach\, we explore post-Lie algebras connected to
multiple zeta values and their q-analogues. For multiple zeta values\, thi
s framework yields an algebraic interpretation of the Goncharov coproduct.
Assuming that the Bernoulli numbers satisfy the so called threshold shuff
le identities\, we present a post-Lie structure\, whose induced Lie bracke
t we expect to restrict to the dual of indecomposables of multiple q-zeta
values.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Clemente (University of Warsaw)
DTSTART:20250919T130000Z
DTEND:20250919T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/57
DESCRIPTION:Title: Algorithmic analysis of control systems with affine input and polyno
mial state dynamics\nby Lorenzo Clemente (University of Warsaw) as par
t of Algebraic and Combinatorial Perspectives in the Mathematical Sciences
\n\n\nAbstract\nWe provide simple algorithms for the formal analysis of de
terministic continuous-time control systems whose dynamics is affine in th
e input and polynomial in the state (in short\, polynomial systems). We co
nsider the following semantic properties: input-output equivalence\, input
independence\, linearity\, and analyticity. Our approach is based on Chen
-Fliess series\, which provide a unique representation of the dynamics of
such systems via their generating series (in noncommuting indeterminates).
Our starting point is Fliess' seminal work showing how the semantic prope
rties above are mirrored by corresponding combinatorial properties on gene
rating series. Next\, we observe that the generating series of polynomial
systems coincide with the class of shuffle-finite series\, a nonlinear gen
eralisation of Schützenberger's rational series which we have recently st
udied in the context of automata theory and enumerative combinatorics. We
exploit and extend recent results in the algorithmic analysis of shufflef-
finite series to show that the semantic properties above are decidable for
polynomial systems.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Lionni (ENS Lyon)
DTSTART:20251003T130000Z
DTEND:20251003T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/58
DESCRIPTION:by Luca Lionni (ENS Lyon) as part of Algebraic and Combinatori
al Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Crew (National Tsing Hua University)
DTSTART:20250905T130000Z
DTEND:20250905T140000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/59
DESCRIPTION:Title: Quantum path signatures\nby Samuel Crew (National Tsing Hua Univ
ersity) as part of Algebraic and Combinatorial Perspectives in the Mathema
tical Sciences\n\n\nAbstract\nI discuss recent work on quantum path signat
ures that places path signatures and associated kernels in a physical gaug
e-theoretic context. Specifically\, I will introduce random unitary develo
pments of smooth paths and derive governing integro-differential that gene
ralise loop equations from random matrix theory. I will discuss a quantum
circuit construction and a sparse GUE ensemble that give rise to an effici
ent quantum algorithm in the one clean qubit model to compute the developm
ent.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Razvan Gurau (Universität Heidelberg)
DTSTART:20251031T140000Z
DTEND:20251031T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/60
DESCRIPTION:by Razvan Gurau (Universität Heidelberg) as part of Algebraic
and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract:
TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Strunck (Evercot AI)
DTSTART:20251114T140000Z
DTEND:20251114T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/61
DESCRIPTION:by Alexander Strunck (Evercot AI) as part of Algebraic and Com
binatorial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Fevola (MATHEXP INRIA Saclay)
DTSTART:20251128T140000Z
DTEND:20251128T150000Z
DTSTAMP:20260419T091208Z
UID:ACPMS/62
DESCRIPTION:by Claudia Fevola (MATHEXP INRIA Saclay) as part of Algebraic
and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract: T
BA\n
LOCATION:
END:VEVENT
END:VCALENDAR