Joint work with Markus Kirschmer\, Fabien Narbonne and Damien Robert

\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabien Pazuki (Copenhagen) DTSTART;VALUE=DATE-TIME:20200521T170000Z DTEND;VALUE=DATE-TIME:20200521T180000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/3 DESCRIPTION:Title: Regulators of number fields and abelian varieties\nby Fabien P azuki (Copenhagen) as part of SFU NT-AG seminar\n\n\nAbstract\nIn the gene ral study of regulators\, we present three inequalities. We first bound fr om below the regulators of number fields\, following previous works of Sil verman and Friedman. We then bound from below the regulators of Mordell-We il groups of abelian varieties defined over a number field\, assuming a co njecture of Lang and Silverman. Finally we explain how to prove an uncondi tional statement for elliptic curves of rank at least 4. This third inequa lity is joint work with Pascal Autissier and Marc Hindry. We give some cor ollaries about the Northcott property and about a counting problem for rat ional points on elliptic curves.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (SFU) DTSTART;VALUE=DATE-TIME:20200528T223000Z DTEND;VALUE=DATE-TIME:20200528T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/4 DESCRIPTION:Title: Fano schemes for complete intersections in toric varieties\nby Nathan Ilten (SFU) as part of SFU NT-AG seminar\n\n\nAbstract\nThe study of the set of lines contained in a fixed hypersurface is classical: Cayley and Salmon showed in 1849 that a smooth cubic surface contains 27 lines\, and Schubert showed in 1879 that a generic quintic threefold contains 287 5 lines. More generally\, the set of k-dimensional linear spaces contained in a fixed projective variety X itself is called the k-th Fano scheme of X. These Fano schemes have been studied extensively when X is a general hy persurface or complete intersection in projective space.\n\nIn this tal k\, I will report on work with Tyler Kelly in which we study Fano schemes for hypersurfaces and complete intersections in projective toric varieties . In particular\, I'll give criteria for the Fano schemes of generic compl ete intersections in a projective toric\nvariety to be non-empty and of "e xpected dimension". Combined with some intersection theory\, this can be u sed for enumerative problems\, for example\, to show that a general degree (3\,3)-hypersurface in the Segre embedding of $\\mathbb{P}^2\\times \\mat hbb{P}^2$ contains exactly 378 lines.

\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Türkü Özlüm Çelik (Leipzig University) DTSTART;VALUE=DATE-TIME:20200604T223000Z DTEND;VALUE=DATE-TIME:20200604T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/5 DESCRIPTION:Title: The Dubrovin threefold of an algebraic curve\nby Türkü Özl üm Çelik (Leipzig University) as part of SFU NT-AG seminar\n\n\nAbstract \nThe solutions to the Kadomtsev-Petviashvili equation that arise from a f ixed\ncomplex algebraic curve are parametrized by a threefold in a weighte d projective space\,\nwhich we name after Boris Dubrovin. Current methods from nonlinear algebra are applied\nto study parametrizations and defining ideals of Dubrovin threefolds. We highlight the\ndichotomy between transc endental representations and exact algebraic computations.\nThis is joi nt work with Daniele Agostini and Bernd Sturmfels.

\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jake Levinson (University of Washington) DTSTART;VALUE=DATE-TIME:20200611T223000Z DTEND;VALUE=DATE-TIME:20200611T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/6 DESCRIPTION:Title: Boij-Söderberg Theory for Grassmannians\nby Jake Levinson (Un iversity of Washington) as part of SFU NT-AG seminar\n\n\nAbstract\nThe Be tti table of a graded module over a polynomial ring encodes much of its st ructure and that of the corresponding sheaf on projective space. In genera l\, it is hard to tell which integer matrices can arise as Betti tables. A n easier problem is to describe such tables up to positive scalar multiple : this is the "cone of Betti tables". The Boij-Söderberg conjectures\, pr oven by Eisenbud-Schreyer\, gave a beautiful description of this cone and\ , as a bonus\, a "dual" description of the cone of cohomology tables of sh eaves.\n\nI will describe some extensions of this theory\, joint with N icolas Ford and Steven Sam\, to the setting of GL-equivariant modules over coordinate rings of matrices. Here\, the dual theory (in geometry) concer ns sheaf cohomology on Grassmannians. One theorem of interest is an equiva riant analog of the Boij-Söderberg pairing between Betti tables and cohom ology tables. This is a bilinear pairing of cones\, with output in the con e coming from the "base case" of square matrices\, which we also fully cha racterize.

\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Avinash Kulkarni (Darmouth) DTSTART;VALUE=DATE-TIME:20200625T223000Z DTEND;VALUE=DATE-TIME:20200625T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/7 DESCRIPTION:Title: pNumerical Linear Algebra\nby Avinash Kulkarni (Darmouth) as p art of SFU NT-AG seminar\n\n\nAbstract\nIn this talk\, I will present new algorithms\, based on ideas from numerical analysis\, for efficiently comp uting the generalized eigenspaces of a square matrix with finite precision p-adic entries. I will then discuss how these eigenvector methods can be used to compute the (approximate) solutions to a zero-dimensional polynomi al system.\n\n(Some content ongoing work with T. Vaccon)\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Turchetti (Dalhousie) DTSTART;VALUE=DATE-TIME:20200702T223000Z DTEND;VALUE=DATE-TIME:20200702T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/8 DESCRIPTION:Title: Moduli spaces of Mumford curves over Z\nby Daniele Turchetti ( Dalhousie) as part of SFU NT-AG seminar\n\n\nAbstract\nSchottky uniformiza tion is the description of an analytic curve as the quotient of an open de nse subset of the projective line by the action of a Schottky group.\nAll complex curves admit this uniformization\, as well as some $p$-adic curves \, called Mumford curves.\nIn this talk\, I present a construction ofAfter introducing Poinea u's theory from scratch\, I will describe universal Mumford curves and exp lain how these can be used as a framework to study the Tate curve and to g ive higher genus generalizations of it. This is based on joint work with J érôme Poineau.

\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Várilly-Alvarado (Rice University) DTSTART;VALUE=DATE-TIME:20200709T223000Z DTEND;VALUE=DATE-TIME:20200709T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/9 DESCRIPTION:Title: Rational surfaces and locally recoverable codes\nby Anthony V árilly-Alvarado (Rice University) as part of SFU NT-AG seminar\n\n\nAbstr act\nMotivated by large-scale storage problems around data loss\, a buddin g branch of coding theory has surfaced in the last decade or so\, centered around locally recoverable codes. These codes have the property that indi vidual symbols in a codeword are functions of other symbols in the same wo rd. If a symbol is lost (as opposed to corrupted)\, it can be recomputed\, and hence a code word can be repaired. Algebraic geometry has a role to p lay in the design of codes with locality properties. In this talk I will e xplain how to use algebraic surfaces birational to the projective plane to both reinterpret constructions of optimal codes already found in the lite rature\, and to find new locally recoverable codes\, many of which are opt imal (in a suitable sense). This is joint work with Cecília Salgado and F elipe Voloch.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Bianca Viray (University of Washington) DTSTART;VALUE=DATE-TIME:20200716T223000Z DTEND;VALUE=DATE-TIME:20200716T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/10 DESCRIPTION:Title: Isolated points on modular curves\nby Bianca Viray (Universit y of Washington) as part of SFU NT-AG seminar\n\n\nAbstract\nFaltings's th eorem on rational points on subvarieties of\nabelian varieties can be used to show that all but finitely many\nalgebraic points on a curve arise in families parametrized by $\\mathbb{P}^1$ or\npositive rank abelian varieti es\; we call these finitely many\nexceptions isolated points. We study ho w isolated points behave under\nmorphisms and then specialize to the case of modular curves. We show\nthat isolated points on $X_1(n)$ push down to isolated points on a\nmodular curve whose level is bounded by a constant that depends only\non the j-invariant of the isolated point. This is join t work with A.\nBourdon\, O. Ejder\, Y. Liu\, and F. Odumodu.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Brendan Creutz (University of Canterbury) DTSTART;VALUE=DATE-TIME:20200723T223000Z DTEND;VALUE=DATE-TIME:20200723T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/11 DESCRIPTION:Title: Brauer-Manin obstructions on constant curves over global function fields\nby Brendan Creutz (University of Canterbury) as part of SFU N T-AG seminar\n\n\nAbstract\nFor a curve C over a global field K it has bee n conjectured that the Brauer-Manin obstruction explains all failures of t he Hasse principle. I will discuss results toward this conjecture in the c ase of constant curves over a global function field\, i.e. where C and D a re curves over a finite field and we consider C over the function field of D. This is joint work with Felipe Voloch.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosa Winter (MPI MiS) DTSTART;VALUE=DATE-TIME:20201029T163000Z DTEND;VALUE=DATE-TIME:20201029T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/12 DESCRIPTION:Title: Density of rational points on a family of del Pezzo surfaces of d egree $1$\nby Rosa Winter (MPI MiS) as part of SFU NT-AG seminar\n\n\n Abstract\nDel Pezzo surfaces are classified by their degree d\, which is a n integer between $1$ and $9$ (for $d ≥ 3$\, these are the smooth surfac es of degree $d$ in $\\mathbb{P}^d$). For del Pezzo surfaces of degree at least $2$ over a field $k$\, we know that the set of $k$-rational points i s Zariski dense provided that the surface has one $k$-rational point to st art with (that lies outside a specific subset of the surface for degree $2 $). However\, for del Pezzo surfaces of degree $1$ over a field k\, even t hough we know that they always contain at least one $k$-rational point\, w e do not know if the set of $k$-rational points is Zariski dense in genera l. I will talk about a result that is joint work with Julie Desjardins\, i n which we give necessary and sufficient conditions for the set of $k$-rat ional points on a specific family of del Pezzo surfaces of degree $1$ to b e Zariski dense\, where k is a number field. I will compare this to previo us results.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Enis Kaya (University of Groningen) DTSTART;VALUE=DATE-TIME:20201105T173000Z DTEND;VALUE=DATE-TIME:20201105T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/13 DESCRIPTION:Title: Explicit Vologodsky Integration for Hyperelliptic Curves\nby Enis Kaya (University of Groningen) as part of SFU NT-AG seminar\n\n\nAbst ract\nLet $X$ be a curve over a $p$-adic field with semi-stable reduction and let $\\omega$ be a \nmeromorphic $1$-form on $X$. There are two notion s of p-adic integration one may associate \nto this data: the Berkovich– Coleman integral which can be performed locally\; and the \nVologodsky int egral with desirable number-theoretic properties. In this talk\, we presen t a \ntheorem comparing the two\, and describe an algorithm for computing Vologodsky integrals \nin the case that $X$ is a hyperelliptic curve. We a lso illustrate our algorithm with a numerical \nexample computed in Sage. This talk is partly based on joint work with Eric Katz.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Elisa Lorenzo García (Universtiy of Rennes 1) DTSTART;VALUE=DATE-TIME:20201112T173000Z DTEND;VALUE=DATE-TIME:20201112T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/14 DESCRIPTION:Title: Primes of bad reduction for CM curves of genus 3 and their expone nts on the discriminant\nby Elisa Lorenzo García (Universtiy of Renne s 1) as part of SFU NT-AG seminar\n\n\nAbstract\nLet O be an order in a se xtic CM field. In order to construct genus 3 curves whose Jacobian has CM by O we need to construct class polynomials\, and for doing this we need t o control the primes in the discriminant of the curves and their exponents . In previous works I studied the so-called "embedding problem" in order t o bound the primes of bad reduction. In the present one we give an algorit hm to explicitly compute them and we bound the exponent of those primes in the discriminant for the hyperelliptic case. Several examples will be giv en.\n\n(joint work with S. Ionica\, P. Kilicer\, K. Lauter\, A. Manzateanu and C. Vincent)\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Sertöz (Max Planck Institute for Mathematics) DTSTART;VALUE=DATE-TIME:20201126T173000Z DTEND;VALUE=DATE-TIME:20201126T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/15 DESCRIPTION:Title: Separating periods of quartic surfaces\nby Emre Sertöz (Max Planck Institute for Mathematics) as part of SFU NT-AG seminar\n\n\nAbstra ct\nKontsevich--Zagier periods form a natural number system that extends t he algebraic numbers by adding constants coming from geometry and physics. Because there are countably many periods\, one would expect it to be poss ible to compute effectively in this number system. This would require an e ffective height function and the ability to separate periods of bounded he ight\, neither of which are currently possible.\n\nIn this talk\, we intro duce an effective height function for periods of quartic surfaces defined over algebraic numbers. We also determine the minimal distance between per iods of bounded height on a single surface. We use these results to prove heuristic computations of Picard groups that rely on approximations of per iods. Moreover\, we give explicit Liouville type numbers that can not be t he ratio of two periods of a quartic surface. This is ongoing work with Pi erre Lairez (Inria\, France).\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Monagan (Simon Fraser University) DTSTART;VALUE=DATE-TIME:20201119T173000Z DTEND;VALUE=DATE-TIME:20201119T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/16 DESCRIPTION:Title: The Tangent-Graeffe root finding algorithm\nby Michael Monaga n (Simon Fraser University) as part of SFU NT-AG seminar\n\n\nAbstract\nLe t $f(x)$ be a polynomial of degree $d$ over a prime field of size $p$.\nSu ppose $f(x)$ has $d$ distinct roots in the field and we want to compute th em.\nQuestion: How fast can we compute the roots?\n\nThe most well known m ethod is the Cantor-Zassenhaus algorithm from 1981.\nIt is implemented in Maple and Magma. It does\, on average\, $O(M(d) \\log d \\log p)$\narithm etic operations in the field where $M(d)$ is the cost of multiplying two \ npolynomials of degree $\\le d$.\n\nIn 2015 Grenet\, van der Hoeven and Le cerf found a beautiful new method for \nthe case $p = s 2^k + 1$ with $s \ \in O(d)$.\nThe new method improves on Cantor-Zassenhaus by a factor of $O (\\log d)$.\nOur contribution is a speed up for the core computation of th e new\nmethod by a constant factor and a C implementation of the new metho d\nusing asymptotically fast polynomial arithmetic.\n\nIn the talk I will present the main ideas behind the new Tangent-Graeffe algorithm\,\nsome ti mings comparing the Tangent Graeffe algorithm with the Cantor-Zassenhaus \ nalgorithm in Magma\, and a new polynomial factorization world record.\n\n This is joint work with Joris van der Hoeven.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Marseglia (Utrecht University) DTSTART;VALUE=DATE-TIME:20201203T173000Z DTEND;VALUE=DATE-TIME:20201203T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/17 DESCRIPTION:Title: Products and Polarizations of Super-Isolated Abelian Varieties\nby Stefano Marseglia (Utrecht University) as part of SFU NT-AG seminar\ n\n\nAbstract\nSuper-isolated abelian varieties are abelian varieties over finite fields whose isogeny class contains a single isomorphism class. In this talk we will review their properties\, consider their products and\, in the ordinary case\, we will describe their (principal) polarizations.\ n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Agostini (MPI MiS) DTSTART;VALUE=DATE-TIME:20201210T173000Z DTEND;VALUE=DATE-TIME:20201210T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/18 DESCRIPTION:Title: On the irrationality of moduli spaces of K3 surfaces\nby Dani ele Agostini (MPI MiS) as part of SFU NT-AG seminar\n\n\nAbstract\nIn this talk\, we consider quantitative measures of irrationality for moduli\nspa ces of polarized K3 surfaces of genus g. We show that\, for infinitely man y examples\,\nthe degree of irrationality is bounded polynomially in terms of g\, so that these spaces become more \nirrational\, but not too fast. The key insight is that the irrationality is bounded by the coefficients \ nof a certain modular form of weight 11. This is joint work with Ignacio B arros and Kuan-Wen Lai.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeline Brandt (Brown University) DTSTART;VALUE=DATE-TIME:20210121T173000Z DTEND;VALUE=DATE-TIME:20210121T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/19 DESCRIPTION:Title: Top Weight Cohomology of $A_g$\nby Madeline Brandt (Brown Uni versity) as part of SFU NT-AG seminar\n\n\nAbstract\nI will discuss a rece nt project in computing the top weight cohomology of the moduli space $A_g $ of principally polarized abelian varieties of dimension $g$ for small va lues of $g$. This piece of the cohomology is controlled by the combinatori cs of the boundary strata of a compactification of $A_g$. Thus\, it can be computed combinatorially. This is joint work with Juliette Bruce\, Melody Chan\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Anwesh Ray (University of British Columbia) DTSTART;VALUE=DATE-TIME:20210128T173000Z DTEND;VALUE=DATE-TIME:20210128T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/20 DESCRIPTION:Title: Level Lowering via the Deformation theory of Galois Representatio ns\nby Anwesh Ray (University of British Columbia) as part of SFU NT-A G seminar\n\n\nAbstract\nElliptic curves defined over the rational numbers arise from \ncertain modular forms. This is the celebrated Modularity the orem of Wiles \net al. Prior to this development\, Ribet had proved a leve l lowering \ntheorem\, thanks to which one is able to optimize the level o f the modular \nform in question. Ribet's theorem combined with the modula rity theorem of \nWiles together imply Fermat's Last theorem.\n\nIn joint work with Ravi Ramakrishna\, we develop some new techniques to\nprove leve l lowering results for more general Galois representations.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Heaton (The Fields Institute) DTSTART;VALUE=DATE-TIME:20210225T173000Z DTEND;VALUE=DATE-TIME:20210225T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/21 DESCRIPTION:Title: Catastrophe discriminants of tensegrity frameworks\nby Alex H eaton (The Fields Institute) as part of SFU NT-AG seminar\n\n\nAbstract\nW e discuss elastic tensegrity frameworks made from rigid bars and elastic c ables\, depending on many parameters. For any fixed parameter values\, the stable equilibrium position of the framework is determined by minimizing an energy function subject to algebraic constraints. As parameters smoothl y change\, it can happen that a stable equilibrium disappears. This loss o f equilibrium is called `catastrophe' since the framework will experience large-scale shape changes despite small changes of parameters. Using nonli near algebra we characterize a semialgebraic subset of the parameter space \, the catastrophe set\, which detects the merging of local extrema from t his parametrized family of constrained optimization problems\, and hence d etects possible catastrophe. Tools from numerical nonlinear algebra allow reliable and efficient computation of all stable equilibrium positions as well as the catastrophe set itself.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Fanelli DTSTART;VALUE=DATE-TIME:20210204T173000Z DTEND;VALUE=DATE-TIME:20210204T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/22 DESCRIPTION:Title: Del Pezzo fibrations in positive characteristic\nby Andrea Fa nelli as part of SFU NT-AG seminar\n\n\nAbstract\nIn this talk\, I will di scuss some pathologies for the generic fibre of del Pezzo fibrations in ch aracteristic $p>0$\, \nmotivated by the recent developments of the MMP in positive characteristic. The recent joint work with \nStefan Schröer appl ies to deduce information on the structure of 3-dimensional Mori fibre spa ces and\nanswers an old question by János Kollár.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Elina Robeva (University of British Columbia) DTSTART;VALUE=DATE-TIME:20210415T163000Z DTEND;VALUE=DATE-TIME:20210415T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/23 DESCRIPTION:Title: Hidden Variables in Linear Causal Models\nby Elina Robeva (Un iversity of British Columbia) as part of SFU NT-AG seminar\n\n\nAbstract\n Identifying causal relationships between random variables from observation al data is an important hard problem in many areas of data science. The pr esence of hidden variables\, though quite realistic\, pauses a variety of further problems. Linear structural equation models\, which express each v ariable as a linear combination of all of its parent variables\, have long been used for learning causal structure from observational data. Surprisi ngly\, when the variables in a linear structural equation model are non-Ga ussian the full causal structure can be learned without interventions\, wh ile in the Gaussian case one can only learn the underlying graph up to a M arkov equivalence class. In this talk\, we first discuss how one can use h igh-order cumulant information to learn the structure of a linear non-Gaus sian structural equation model with hidden variables. While prior work pos its that each hidden variable is the common cause of two observed variable s\, we allow each hidden variable to be the common cause of multiple obser ved variables. Next\, we discuss hidden variable Gaussian causal models an d the difficulties that arise with learning those. We show it is hard to e ven describe the Markov equivalence classes in this case\, and we give a s emi algebraic description of a large class of these models.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Lian Duan (Colorado State University) DTSTART;VALUE=DATE-TIME:20210408T163000Z DTEND;VALUE=DATE-TIME:20210408T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/24 DESCRIPTION:Title: Bertini's theorem over finite field and Frobenius nonclassical va rieties\nby Lian Duan (Colorado State University) as part of SFU NT-AG seminar\n\n\nAbstract\nLet X be a smooth subvariety of $\\mathbb{P}^n$ de fined over a field k. Suppose k is an infinite field\, then the classical theorem of Bertini asserts that X admits a smooth hyperplane section. Howe ver\, if k is a finite field\, there are examples of X such that every hyp erplane H in $\\mathbb{P}^n$ defined over k is tangent to X. One of the re medies in this situation is to extending the ground field k to its finite extension\, and considering all the hyperplanes defined over the extension field. Then one can ask: Knowing the invariants of X (e.g. the degree of X)\, how much one needs to extend k in order to guarantee at least one tr ansverse hyperplane section? In this talk we will report several results r egarding to this type of questions. We also want to talk about a special t ype of varieties (Frobenius nonclassical varieties) that appear naturally in our research. This is a joint work with Shamil Asgarli and Kuan-Wen Lai .\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Alp Bassa (Boğaziçi University) DTSTART;VALUE=DATE-TIME:20210304T173000Z DTEND;VALUE=DATE-TIME:20210304T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/25 DESCRIPTION:Title: Rational points on curves over finite fields and their asymptotic \nby Alp Bassa (Boğaziçi University) as part of SFU NT-AG seminar\n\ n\nAbstract\nCurves over finite fields with many rational points have been of interest for both theoretical reasons and for applications. To obtain such curves with large genus various methods have been employed in the pas t. One such method is by means of explicit recursive equations and will be the emphasis of this talk. The recursive nature of these towers makes the m very special and in fact all good examples have been shown to have a mod ular interpretation of some sort. In this talk I will try to give an overv iew of the landscape of explicit recursive towers and their modularity.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Asher Auel (Dartmouth College) DTSTART;VALUE=DATE-TIME:20210318T163000Z DTEND;VALUE=DATE-TIME:20210318T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/26 DESCRIPTION:Title: The local-global principle for quadratic forms over function fiel ds\nby Asher Auel (Dartmouth College) as part of SFU NT-AG seminar\n\n \nAbstract\nThe Hasse-Minkowski theorem says that a quadratic form over a global field admits a nontrivial zero if it admits a nontrivial zero every where locally. Over more general fields of arithmetic and geometric intere st\, the failure of the local-global principle is often controlled by auxi liary structures of interest\, such as torsion points of the Jacobian and the Brauer group. I will explain work with V. Suresh on the failure of th e local-global principle for quadratic forms over function fields varietie s of dimension at least two. The counterexamples we construct are control led by higher unramified cohomology groups and involve the study of Calabi -Yau varieties of generalized Kummer type that originally arose from numbe r theory. Along the way\, we need to develop an arithmetic version of a r esult of Gabber on the nontriviality of certain unramified cohomology clas ses on products of elliptic curves.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Ari Shnidman (Hebrew University of Jerusalem) DTSTART;VALUE=DATE-TIME:20210325T163000Z DTEND;VALUE=DATE-TIME:20210325T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/27 DESCRIPTION:Title: Selmer groups of abelian varieties with cyclotomic multiplication \nby Ari Shnidman (Hebrew University of Jerusalem) as part of SFU NT-A G seminar\n\n\nAbstract\nLet $A$ be an abelian variety over a number field $F$\, with complex multiplication by the $n$-th cyclotomic field $\\mathb b{Q}(\\zeta)$. If $n = 3^m$\, we show that the average size of the $(1- \\zeta)$-Selmer group of $A_d$\, as $A_d$ varies through the twist family of $A$\, is equal to 2. As a corollary\, the average $\\mathbb{Z}[\\zeta ]$-rank of $A_d$ is at most 1/2\, and at least 50% of $A_d$ have rank 0. More generally\, we prove average rank bounds for various twist famili es of abelian varieties with "cyclotomic" multiplication (not necessarily CM) over $\\bar F$\, such as sextic twist families of trigonal Jacobians o ver $\\mathbb{Q}$. These results have application to questions of "rank gain" for a fixed elliptic curve over a family of sextic fields\, as well as the distribution of $\\#C_d(F)$\, as $C_d$ varies through twists of a f ixed curve $C$ of genus $ g > 1$. This is joint work with Ariel Weiss.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Fevola (MPI MiS) DTSTART;VALUE=DATE-TIME:20210311T173000Z DTEND;VALUE=DATE-TIME:20210311T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/28 DESCRIPTION:Title: KP Solitons from Tropical Limits\nby Claudia Fevola (MPI MiS) as part of SFU NT-AG seminar\n\n\nAbstract\nIn this talk\, we present sol utions to the Kadomtsev-Petviashvili equation whose underlying algebraic c urves undergo tropical degenerations. Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We intro duce the Hirota variety which parametrizes all tau functions arising from such a sum. After introducing solitons solutions\, we compute tau function s from points on the Sato Grassmannian that represent Riemann-Roch spaces. \nThis is joint work with Daniele Agostini\, Yelena Mandelshtam and Bernd Sturmfels.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Tristan Vaccon (Université de Limoges) DTSTART;VALUE=DATE-TIME:20210401T163000Z DTEND;VALUE=DATE-TIME:20210401T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/29 DESCRIPTION:Title: On Gröbner bases over Tate algebras\nby Tristan Vaccon (Univ ersité de Limoges) as part of SFU NT-AG seminar\n\n\nAbstract\nTate serie s are a generalization of polynomials introduced by John Tate in 1962\, wh en defining a p-adic analogue of the correspondence between algebraic geom etry and analytic geometry. This p-adic analogue is called rigid geometry\ , and Tate series\, similar to analytic functions in the complex case\, ar e its fundamental objects. Tate series are defined as multivariate formal power series over a p-adic ring or field\, with a convergence condition on a closed ball.\n\nTate series are naturally approximated by multivariate polynomials over F_p or Z/p^n Z\, and it is possible to define a theory of Gröbner bases for ideals of Tate series\, which opens the way towards ef fective rigid geometry. \n\nIn this talk\, I will present classical algori thms to compute Gröbner bases (Buchberger\, F5\, FGLM) and how they can be adapted for Tate series.\n\nJoint work with Xavier Caruso and Thibaut V erron.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Özlem Ejder (Boğaziçi University) DTSTART;VALUE=DATE-TIME:20210527T163000Z DTEND;VALUE=DATE-TIME:20210527T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/30 DESCRIPTION:Title: Galois theory of Dynamical Belyi Maps\nby Özlem Ejder (Boğa ziçi University) as part of SFU NT-AG seminar\n\n\nAbstract\nLet $f: \\ma thbb{P}^1_K \\rightarrow \\mathbb{P}^1_K$ be a rational map defined over a number field $K$. The Galois theory of the iterates $f^n=f \\circ \\dots \\circ f$ has applications both in number\ntheory and arithmetic dynamics. In this talk\, we will discuss the various Galois groups attached to the iterates of $f$\, namely arithmetic and geometric monodromy groups and Arb oreal Galois representations. While providing a survey of recent results o n the subject\, we will also talk about joint work with I. Bouw and V. Kar emaker on Dynamical Belyi maps.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Lara Bossinger (Instituto de Matemáticas UNAM) DTSTART;VALUE=DATE-TIME:20210610T163000Z DTEND;VALUE=DATE-TIME:20210610T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/31 DESCRIPTION:Title: Projections in toric degenerations and standard monomials\nby Lara Bossinger (Instituto de Matemáticas UNAM) as part of SFU NT-AG semi nar\n\n\nAbstract\nI will report on joint work in progress with Takuya Mur ata. We study toric degenerations\, i.e. flat morphism of a normal variety to the affine line whose generic fibre is isomorphic to a fixed projectiv e variety and whose special fibre is a projective toric variety. Although such a flat morphism may be given abstractly (i.e. without an embedding\, for example a toric scheme over the affine line) using valuations and Grö bner theory we may restrict our attention to the case where our family com es endowed with an embedding. I will illustrate an example of an elliptic curve where a toric degeneration admits a projection from the generic fibr e (the elliptic curve) to the special fibre (the toric curve). We want to understand which kind of (embedded) toric degenerations admit such a proje ction. The notion of standard monomials in Gröbner theory proves to be a useful tool in constructing projections in arbitrary toric degenerations.\ n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Soumya Sankar (Ohio State University) DTSTART;VALUE=DATE-TIME:20210708T163000Z DTEND;VALUE=DATE-TIME:20210708T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/32 DESCRIPTION:Title: Counting elliptic curves with a rational N-isogeny\nby Soumya Sankar (Ohio State University) as part of SFU NT-AG seminar\n\n\nAbstract \nThe classical problem of counting elliptic curves with a rational N-isog eny can be phrased in terms of counting rational points on certain moduli stacks of elliptic curves. Counting points on stacks poses various challen ges\, and I will discuss these along with a few ways to overcome them. I w ill also talk about the theory of heights on stacks developed in recent wo rk of Ellenberg\, Satriano and Zureick-Brown and use it to count elliptic curves with an N-isogeny for certain N. The talk assumes no prior knowledg e of stacks and is based on joint work with Brandon Boggess.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Mateusz Michałek (University of Konstanz) DTSTART;VALUE=DATE-TIME:20210624T163000Z DTEND;VALUE=DATE-TIME:20210624T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/33 DESCRIPTION:Title: Chromatic polynomials of tensors and cohomology of complete forms \nby Mateusz Michałek (University of Konstanz) as part of SFU NT-AG s eminar\n\n\nAbstract\nThere are two plane quadrics passing through four ge neral points and tangent to one general line. There are six ways to proper ly color vertices of a triangle with three colors. The maximum likelihood function for a general linear concentration two dimensional model in a fou r dimensional space has three critical points. Each of these examples of c ourse comes naturally in families.\nIn our talk we will try to explain wha t the above numbers mean\, how to compute them and that they are all shado ws of the same construction. Our methods are based on the cohomology ring of the so-called variety of complete forms.\nThe talk is based on works wi th Conner\, Dinu\, Manivel\, Monin\, Seynnaeve\, Wisniewski and Vodicka. T hese are on the other hand based on fundamental works due to Huh\, Pragacz \, Sturmfels\, Teissier\, Uhler and others (Schubert included).\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Melissa Sherman-Bennett (UC Berkeley) DTSTART;VALUE=DATE-TIME:20210715T163000Z DTEND;VALUE=DATE-TIME:20210715T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/34 DESCRIPTION:Title: The hypersimplex and the m=2 amplituhedron: Eulerian numbers\, si gn flips\, triangulations\nby Melissa Sherman-Bennett (UC Berkeley) as part of SFU NT-AG seminar\n\n\nAbstract\nPhysicists Arkhani-Hamed and Trn ka introduced the amplituhedron to better understand scattering amplitudes in N=4 super Yang-Mills theory. The amplituhedron is the image of the tot ally nonnegative Grassmannian under the "amplituhedron map"\, which is ind uced by matrix multiplication. Examples of amplituhedra include cyclic pol ytopes\, the totally nonnegative Grassmannian itself\, and cyclic hyperpla ne arrangements. In general\, the amplituhedron is not a polytope. However \, Lukowski--Parisi--Williams noticed a mysterious connection between the m=2 amplituhedron and the hypersimplex\, and conjectured a correspondence between their fine positroidal subdivisions. I'll discuss joint work with Matteo Parisi and Lauren Williams\, in which we prove one direction of thi s correspondence. Along the way\, we prove an intrinsic description of the m=2 amplituhedron conjectured by Arkhani-Hamed--Thomas--Trnka\; give a de composition of the m=2 amplituhedron into Eulerian number-many sign chambe rs\, in direct analogy to a triangulation of the hypersimplex\; and find n ew cluster varieties in the Grassmannian.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Selvi Kara (University of South Alabama) DTSTART;VALUE=DATE-TIME:20210617T163000Z DTEND;VALUE=DATE-TIME:20210617T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/35 DESCRIPTION:Title: Blow-Up Algebras of Strongly Stable Ideals\nby Selvi Kara (Un iversity of South Alabama) as part of SFU NT-AG seminar\n\n\nAbstract\nLet $S$ be a polynomial ring and $I_1\,\\ldots\, I_r$ be a collection of idea ls in $S$. The multi-Rees algebra $\\mathcal{R} (I_1\,\\ldots\, I_r)$ of t his collection of ideals encode many algebraic properties of these ideals\ , their products\, and powers. Additionally\, the multi-Rees algebra $\\m athcal{R} (I_1\,\\ldots\, I_r)$ arise in successive blowing up of $\\textr m{Spec } S$ at the subschemes defined by $I_1\,\\ldots\, I_r$. Due to this connection\, Rees and multi-Rees algebras are also called blow-up algebra s in the literature.\n\nIn this talk\, we will focus on Rees and multi-Ree s algebras of strongly stable ideals. In particular\, we will discuss the Koszulness of these algebras through a systematic study of these objects v ia three parameters: the number of ideals in the collection\, the number o f Borel generators of each ideal\, and the degrees of Borel generators. In our study\, we utilize combinatorial objects such as fiber graphs to dete ct Gröbner bases and Koszulness of these algebras. This talk is based on a joint work with Kuei-Nuan Lin and Gabriel Sosa.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Yairon Cid-Ruiz (Ghent University) DTSTART;VALUE=DATE-TIME:20210722T163000Z DTEND;VALUE=DATE-TIME:20210722T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/36 DESCRIPTION:Title: Primary decomposition with differential operators.\nby Yairon Cid-Ruiz (Ghent University) as part of SFU NT-AG seminar\n\n\nAbstract\nW e introduce differential primary decompositions for ideals in a commutativ e ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the arithmetic multiplicity. Minima l differential primary decompositions are unique up to change of bases. Ou r results generalize the construction of Noetherian operators for primary ideals in the analytic theory of Ehrenpreis-Palamodov\, and they offer a c oncise method for representing affine schemes. The case of modules is also addressed. This is joint work with Bernd Sturmfels.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Anwesh Ray (University of British Columbia) DTSTART;VALUE=DATE-TIME:20210729T163000Z DTEND;VALUE=DATE-TIME:20210729T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/37 DESCRIPTION:Title: Arithmetic statistics and the Iwasawa theory of elliptic curves\nby Anwesh Ray (University of British Columbia) as part of SFU NT-AG se minar\n\n\nAbstract\nAn elliptic curve defined over the rationals gives ri se to a \ncompatible system of Galois representations. The Iwasawa invaria nts \nassociated to these representations epitomize their arithmetic and I wasawa \ntheoretic properties. The study of these invariants is the subjec t of much \nconjecture and contemplation. For instance\, according to a lo ng-standing \nconjecture of R. Greenberg\, the Iwasawa "mu-invariant" must vanish\, subject \nto mild hypothesis. Overall\, there is a subtle relati onship between the \nbehavior of these invariants and the p-adic Birch and Swinnerton-Dyer \nformula. We study the behaviour of these invariants on average\, where \nelliptic curves over the rationals are ordered according to height. I will \ndiscuss some recent results (joint with Debanjana Kun du) in which we set \nout new directions in arithmetic statistics and Iwas awa theory.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Gillespie (Colorado State University) DTSTART;VALUE=DATE-TIME:20210812T163000Z DTEND;VALUE=DATE-TIME:20210812T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/38 DESCRIPTION:Title: Lazy tournaments\, slide rules\, and multidegrees of projective e mbeddings of M_{0\,n}-bar\nby Maria Gillespie (Colorado State Universi ty) as part of SFU NT-AG seminar\n\n\nAbstract\nWe present a combinatorial algorithm on trivalent trees that we call a lazy tournament\, which gives rise to a new geometric interpretation of the multidegrees of a projectiv e embedding of the moduli space M_{0\,n}-bar of stable n-marked genus 0 cu rves. We will show that the multidegrees are enumerated by disjoint sets of boundary points of the moduli space that can be seen to total (2n-7)!!\ , giving a natural proof of the value of the total degree. These sets are compatible with the forgetting maps used to derive the previously known r ecursion for the multidegrees.\n\nAs time permits\, we will discuss an alt ernative combinatorial construction of (non-disjoint) sets of boundary poi nts that enumerate the multidegrees\, via slide rules\, that can in fact b e achieved geometrically via a degeneration of intersections with hyperpla nes in the projective embedding. These combinatorial rules further genera lize to give a positive expansion of any product of psi or omega classes o n M_{0\,n}-bar in terms of boundary strata.\n\nThis is joint work with Sea n Griffin and Jake Levinson.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Vance Blankers (Northeastern University) DTSTART;VALUE=DATE-TIME:20210916T163000Z DTEND;VALUE=DATE-TIME:20210916T173000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/39 DESCRIPTION:Title: Alternative compactifications of the moduli space of curves\n by Vance Blankers (Northeastern University) as part of SFU NT-AG seminar\n \n\nAbstract\nThe moduli space of curves is an important object in modern algebraic geometry\, both interesting in its own right and serving as a te st space for broader geometric programs. These often require the space to be compact\, which leads to a variety of choices for compactification\, th e most well-known of which is the Deligne-Mumford-Knudsen compactification by stable curves\, originally introduced in 1969. Since then\, several al ternative compactifications have been constructed and studied\, and in 201 3 David Smyth used a combinatorial framework to make progress towards clas sifying all "sufficiently nice" compactifications. In this talk\, I'll dis cuss some of the most well-studied compactifications\, as well as two new compactifications\, which together classify the Gorenstein compactificatio ns in genus 0 and genus 1.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Raymond Cheng (Columbia University) DTSTART;VALUE=DATE-TIME:20211028T223000Z DTEND;VALUE=DATE-TIME:20211028T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/40 DESCRIPTION:Title: Unbounded negativity on rational surfaces in positive characteris tic\nby Raymond Cheng (Columbia University) as part of SFU NT-AG semin ar\n\n\nAbstract\nFix your favourite smooth projective surface S and wonde r: how negative can the self-intersection of a curve in S be? Apparently\, there are situations in which curves might not actually get so negative: an old folklore conjecture\, nowadays known as the Bounded Negativity Conj ecture\, predicts that if S were defined over the complex numbers\, then t he self-intersection of any curve in S is bounded below by a constant depe nding only on S. If\, however\, S were defined over a field of positive ch aracteristic\, then it is known that the Bounded Negativity Conjecture as stated cannot hold. For a long time\, however\, it was not known whether t he Conjecture failed for rational surfaces in positive characteristic. In this talk\, I describe the first examples of rational surfaces failing Bou nded Negativity which I constructed with Remy van Dobben de Bruyn earlier this year.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Shabnam Akhtari (University of Oregon) DTSTART;VALUE=DATE-TIME:20211118T233000Z DTEND;VALUE=DATE-TIME:20211119T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/41 DESCRIPTION:Title: Orders in cubic and quartic number fields and classical Diophanti ne equations\nby Shabnam Akhtari (University of Oregon) as part of SFU NT-AG seminar\n\n\nAbstract\nAn order $\\mathcal{O}$ in an algebraic numb er field is called monogenic if over $\\mathbb{Z}$ it can be generated by one element. Győry has shown that there are finitely equivalence classes $\\alpha \\in \\mathcal{O}$ such that $\\mathcal{O} = \\mathbb{Z}[\\alpha] $\, where two algebraic integers $\\alpha\, \\alpha'$ are called equivalen t if $\\alpha + \\alpha'$ or $\\alpha - \\alpha'$ is a rational integer. A n interesting problem is to count the number of monogenizations of a given monogenic order. First we will note\, for a given order $\\mathcal{O}$\, that $$\\mathcal{O} = \\mathbb{Z}[\\alpha] \\text{ in } \\alpha$$ is indee d a Diophantine equation. Then we will discuss how some old algorithmic re sults can be used to obtain new and improved upper bounds for the number o f monogenizations of a cubic or quartic order.\n\nThis talk should be acce ssible to any math graduate student and\nquestions about basic concepts ar e welcome. We will start by recalling\nsome definitions from elementary al gebraic number theory. Number\nfields\, lattices over $\\mathbb{Z}$\, and simple polynomial equations are the main\nfocus of this talk.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Escobar (Washington University in St. Louis) DTSTART;VALUE=DATE-TIME:20211104T223000Z DTEND;VALUE=DATE-TIME:20211104T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/42 DESCRIPTION:Title: Determining the complexity of Kazhdan-Lusztig varieties\nby L aura Escobar (Washington University in St. Louis) as part of SFU NT-AG sem inar\n\n\nAbstract\nKazhdan-Lusztig varieties are defined by ideals genera ted by certain minors of a matrix\, which are chosen by a combinatorial ru le. These varieties are of interest in commutative algebra and Schubert va rieties. Each Kazhdan-Lusztig variety has a natural torus action from whic h one can construct a cone. The complexity of this torus action can be com puted from the dimension of the cone and\, in some sense\, indicates how c lose the variety is to the toric variety of the cone. In joint work with M aria Donten-Bury and Irem Portakal we address the problem of classifying w hich Kazhdan-Lusztig varieties have a given complexity. We do so by utiliz ing the rich combinatorics of Kazhdan-Lusztig varieties.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Habiba Kadiri (University of Lethbridge) DTSTART;VALUE=DATE-TIME:20211021T223000Z DTEND;VALUE=DATE-TIME:20211021T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/44 DESCRIPTION:Title: Primes in the Chebotarev density theorem for all number fields\nby Habiba Kadiri (University of Lethbridge) as part of SFU NT-AG semina r\n\nLecture held in AQ 4145.\n\nAbstract\nLet $L/K$ be a Galois extension of number fields such that $L\\not=\\mathbb{Q}$\, and let $C$ be a conjug acy class in the Galois group of $L/K$. We show that there exists an unram ified prime $\\mathfrak{p}$ of $K$ such that $\\sigma_{\\mathfrak{p}}=C$ a nd $N \\mathfrak{p} \\le d_{L}^{B}$ with $B= 310$. This improves a previou s result of Ahn and Kwon\, who showed that $B=12\\\,577$ is admissible. Th e main tool is a stronger Deuring-Heilbronn (zero-repulsion) phenomenon. W e also use Fiori's numerical verification for a finite list of fields. Thi s is joint work with Peng-Jie Wong (NCTS\, Taiwan).\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabel Vogt (Brown University) DTSTART;VALUE=DATE-TIME:20211209T233000Z DTEND;VALUE=DATE-TIME:20211210T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/45 DESCRIPTION:Title: Brill--Noether Theory over the Hurwitz space\nby Isabel Vogt (Brown University) as part of SFU NT-AG seminar\n\n\nAbstract\nLet C be a curve of genus g. A fundamental problem in the theory of algebraic curves is to understand maps of C to projective space of dimension r of degree d. When the curve C is general\, the moduli space of such maps is well-under stood by the main theorems of Brill--Noether theory. However\, in nature\ , curves C are often encountered already equipped with a map to some proje ctive space\, which may force them to be special in moduli. The simplest case is when C is general among curves of fixed gonality. Despite much st udy over the past three decades\, a similarly complete picture has proved elusive in this case. In this talk\, I will discuss joint work with Eric L arson and Hannah Larson that completes such a picture\, by proving analogs of all of the main theorems of Brill--Noether theory in this setting.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Padmavathi Srinivasan (University of Georgia) DTSTART;VALUE=DATE-TIME:20211202T233000Z DTEND;VALUE=DATE-TIME:20211203T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/46 DESCRIPTION:Title: Some Galois cohomology classes arising from the fundamental group of a curve\nby Padmavathi Srinivasan (University of Georgia) as part of SFU NT-AG seminar\n\n\nAbstract\nWe will first talk about the Ceresa cl ass\, which is the image under a cycle class map of a canonical algebraic cycle associated to a curve in its Jacobian. This class vanishes for all h yperelliptic curves and was expected to be nonvanishing for non-hyperellip tic curves. In joint work with Dean Bisogno\, Wanlin Li and Daniel Litt\, we construct a non-hyperelliptic genus 3 quotient of the Fricke-Macbeath c urve with vanishing Ceresa class\, using the character theory of the autom orphism group of the curve\, namely\, PSL_2(F_8). This will also include t he tale of another explicit genus 3 curve studied by Schoen that was lost and then found again!\n\nTime permitting\, we will also talk about some Ga lois cohomology classes that obstruct the existence of rational points on curves\, by obstructing splittings to natural exact sequences coming from the fundamental group of a curve. In joint work with Wanlin Li\, Daniel Li tt and Nick Salter\, we use these obstruction classes to give a new proof of Grothendieck’s section conjecture for the generic curve of genus g > 2. An analysis of the degeneration of these classes at the boundary of the moduli space of curves\, combined with a specialization argument lets us prove the existence of infinitely many curves of each genus over p-adic fi elds and number fields that satisfy the section conjecture.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (Simon Fraser University) DTSTART;VALUE=DATE-TIME:20210923T223000Z DTEND;VALUE=DATE-TIME:20210923T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/47 DESCRIPTION:Title: Cluster algebras and deformation theory\nby Nathan Ilten (Sim on Fraser University) as part of SFU NT-AG seminar\n\n\nAbstract\nCluster Algebras\, introduced in 2001 by Fomin and Zelevinsky\, are a kind of comm utative ring equipped with special combinatorial structure. They appear in a range of contexts\, from representation theory to mirror symmetry. Afte r providing a gentle introduction to cluster algebras\, I will report on o ne aspect of work-in-progress with Alfredo Nájera Chávez and Hipolito Tr effinger. We show that for cluster algebras of finite type\, the cluster a lgebra with universal coefficients is equal to a canonically identified su bfamily of the semiuniversal family for the Stanley-Reisner ring of the cl uster complex.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ng (University of Lethbridge) DTSTART;VALUE=DATE-TIME:20211007T223000Z DTEND;VALUE=DATE-TIME:20211007T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/51 DESCRIPTION:Title: Moments of the Riemann zeta function\nby Nathan Ng (Universit y of Lethbridge) as part of SFU NT-AG seminar\n\n\nAbstract\nFor over a 10 0 years\, $I_k(T)$\, the $2k$-th moments of the Riemann zeta function on t he critical line have been extensively studied. In 1918 Hardy-Littlewood e stablished an asymptotic formula for the second moment ($k=1$) and in 1926 Ingham established an asymptotic formula for the fourth moment $(k=2)$. S ince then no other moments have been asymptotically evaluated. In the lat e 1990's Keating and Snaith gave a conjecture for the size of $I_k(T)$ bas ed on a random matrix model. Recently I showed that an asymptotic formula for the sixth moment ($k=3$) follows from a conjectural formula for some t ernary additive divisor sums. In this talk I will give an overview of the se results.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Klevdal (University of Utah) DTSTART;VALUE=DATE-TIME:20211014T223000Z DTEND;VALUE=DATE-TIME:20211014T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/52 DESCRIPTION:Title: Integrality of $G$-local systems\nby Christian Klevdal (Unive rsity of Utah) as part of SFU NT-AG seminar\n\n\nAbstract\nSimpson conject ured that for a reductive group $G$\, rigid $G$-local systems on a smooth projective complex variety are integral. I will discuss a proof of integra lity for cohomologically rigid $G$-local systems. This generalizes and is inspired by work of Esnault and Groechenig for $GL_n$. Surprisingly\, the main tools used in the proof (for general $G$ and $GL_n$) are the work of L. Lafforgue on the Langlands program for curves over function fields\, an d work of Drinfeld on companions of $\\ell$-adic sheaves. The major differ ences between general $G$ and $GL_n$ are first to make sense of companions for $G$-local systems\, and second to show that the monodromy group of a rigid G-local system is semisimple. All work is joint with Stefan Patrikis .\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricia Klein (University of Minnesota) DTSTART;VALUE=DATE-TIME:20220113T233000Z DTEND;VALUE=DATE-TIME:20220114T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/53 DESCRIPTION:Title: Bumpless pipe dreams encode Gröbner geometry of Schubert polynom ials\nby Patricia Klein (University of Minnesota) as part of SFU NT-AG seminar\n\n\nAbstract\nKnutson and Miller established a connection betwee n the anti-diagonal Gröbner degenerations of matrix Schubert varieties an d the pre-existing combinatorics of pipe dreams. They used this correspond ence to give a geometrically-natural explanation for the appearance of the combinatorially-defined Schubert polynomials as representatives of Schube rt classes. In this talk\, we will describe a similar connection between d iagonal degenerations of matrix Schubert varieties and bumpless pipe dream s\, newer combinatorial objects introduced by Lam\, Lee\, and Shimozono. T his connection was conjectured by Hamaker\, Pechenik\, and Weigandt. This talk is based on joint work with Anna Weigandt.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/53/ END:VEVENT BEGIN:VEVENT SUMMARY:José González (University of California\, Riverside) DTSTART;VALUE=DATE-TIME:20220203T233000Z DTEND;VALUE=DATE-TIME:20220204T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/56 DESCRIPTION:Title: Generation of jets and Fujita’s jet ampleness conjecture on tor ic varieties\nby José González (University of California\, Riverside ) as part of SFU NT-AG seminar\n\n\nAbstract\nA line bundle is k-jet ample if it has enough global sections to separate points\, tangent vectors\, a nd also their higher order analogues called k-jets. For example\, 0-jet am pleness is equivalent to global generation and 1-jet ampleness is equivale nt to very ampleness. We give sharp bounds guaranteeing that a line bundle on a projective toric variety is k-jet ample in terms of its intersection numbers with the invariant curves\, in terms of the lattice lengths of th e edges of its polytope\, in terms of the higher concavity of its piecewis e linear function and in terms of its Seshadri constant. As an application \, we prove the k-jet generalizations of Fujita’s conjectures on toric v arieties.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Bryan (University of British Columbia) DTSTART;VALUE=DATE-TIME:20220210T233000Z DTEND;VALUE=DATE-TIME:20220211T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/57 DESCRIPTION:Title: Bott periodicity from algebraic geometry\nby Jim Bryan (Unive rsity of British Columbia) as part of SFU NT-AG seminar\n\n\nAbstract\nA f amous theorem in algebraic topology is Bott periodicity: the homotopy grou ps of the space of orthogonal matrices repeat with period 8: pi_k(O) = pi _{k+8}(O) . I will give an elementary overview of Bott periodicity and the n I will explain how to formulate and prove a theorem in algebraic geometr y which\, when specialized to the field of complex numbers\, recovers the usual topological Bott periodicity\, but makes sense over any field. This is work in progress with Ravi Vakil.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Katrina Honigs (Simon Fraser University) DTSTART;VALUE=DATE-TIME:20220217T233000Z DTEND;VALUE=DATE-TIME:20220218T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/58 DESCRIPTION:Title: The fixed locus of a symplectic involution on a hyperkahler 4-fol d of Kummer type\nby Katrina Honigs (Simon Fraser University) as part of SFU NT-AG seminar\n\nLecture held in K-9509.\n\nAbstract\nIn this talk I will discuss work in progress joint with Sarah Frei on symplectic involu tions of hyperkahler manifolds of Kummer type. The fixed loci of these inv olutions correspond to cohomology classes and have very interesting proper ties. The talk will focus on the geometry of such a fixed locus on a parti cular 4-fold.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Juliette Bruce (University of California\, Berkeley) DTSTART;VALUE=DATE-TIME:20220303T233000Z DTEND;VALUE=DATE-TIME:20220304T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/60 DESCRIPTION:Title: Multigraded regularity on products of projective spaces\nby J uliette Bruce (University of California\, Berkeley) as part of SFU NT-AG s eminar\n\n\nAbstract\nEisenbud and Goto described the Castelnuovo-Mumford regularity of a module on projective space in terms of three different pro perties of the corresponding graded module: its betti numbers\, its local cohomology\, and its truncations. For the multigraded generalization of re gularity defined by Maclagan and Smith\, these three conditions are no lon ger equivalent. I will characterize each of them for modules on products o f projective spaces.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Pietromonaco (University of British Columbia) DTSTART;VALUE=DATE-TIME:20220324T223000Z DTEND;VALUE=DATE-TIME:20220324T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/62 DESCRIPTION:Title: Enumerative Geometry of Orbifold K3 Surfaces\nby Stephen Piet romonaco (University of British Columbia) as part of SFU NT-AG seminar\n\n Lecture held in K-9509.\n\nAbstract\nTwo of the most celebrated theorems i n enumerative geometry\n(both predicted by string theorists) surround curv e-counting for K3\nsurfaces. The Yau-Zaslow formula computes the honest nu mber of rational\ncurves in a K3 surface\, and was generalized to the Katz -Klemm-Vafa formula\ncomputing the (virtual) number of curves of any genus . In this talk\, I will\nreview this story and then describe a recent gene ralization to orbifold K3\nsurfaces. One interpretation of the new theory is as producing a virtual\ncount of curves in the orbifold\, where we trac k both the genus of the curve\nand the genus of the corresponding invarian t curve upstairs. As one\nexample\, we generalize the counts of hyperellip tic curves in an Abelian\nsurface carried out by Bryan-Oberdieck-Pandharip ande-Yin. This is work in\nprogress with Jim Bryan.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Masahiro Nakahara (University of Washington) DTSTART;VALUE=DATE-TIME:20220317T223000Z DTEND;VALUE=DATE-TIME:20220317T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/63 DESCRIPTION:Title: Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces\nby Masahiro Nakahara (University of Washing ton) as part of SFU NT-AG seminar\n\n\nAbstract\nA variety satisfies poten tial density if it contains a dense subset of rational points after extend ing its ground field by a finite degree. A collection of varieties satisfi es uniform potential density if that degree can be uniformly bounded. I wi ll discuss this property for connected algebraic groups of a fixed dimensi on and elliptic K3 surfaces. This is joint work with Kuan-Wen Lai.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Marni Mishna (Simon Fraser University) DTSTART;VALUE=DATE-TIME:20220331T223000Z DTEND;VALUE=DATE-TIME:20220331T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/64 DESCRIPTION:Title: Lattice Walk Enumeration: Analytic\, algebraic and geometric aspe cts\nby Marni Mishna (Simon Fraser University) as part of SFU NT-AG se minar\n\nLecture held in K-9509.\n\nAbstract\nThis talk will survey classi fication of lattice path models via their generating functions.. A very cl assic object of combinatorics\, lattice walks withstand study from a varie ty of perspectives. Even the simple task of classifying the two dimensiona l nearest neighbour walks restricted to the first quadrant has brought int o play a surprising diversity of techniques from algebra to analysis to ge ometry. We will consider walks under a few different lenses. We will see h ow lattice walks can naturally guide the classification of functions into categories like algebraic\, D-finite\, differentiably algebraic and beyond . Elliptic curves and differential Galois theory play an important role.\ n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricia Klein (University of Minnesota) DTSTART;VALUE=DATE-TIME:20220407T223000Z DTEND;VALUE=DATE-TIME:20220407T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/65 DESCRIPTION:Title: Bumpless pipe dreams encode Gröbner geometry of Schubert polynom ials\nby Patricia Klein (University of Minnesota) as part of SFU NT-AG seminar\n\n\nAbstract\nKnutson and Miller established a connection betwee n the anti-diagonal Gröbner degenerations of matrix Schubert varieties an d the pre-existing combinatorics of pipe dreams. They used this correspond ence to give a geometrically-natural explanation for the appearance of the combinatorially-defined Schubert polynomials as representatives of Schube rt classes. In this talk\, we will describe a similar connection between d iagonal degenerations of matrix Schubert varieties and bumpless pipe dream s\, newer combinatorial objects introduced by Lam\, Lee\, and Shimozono. T his connection was conjectured by Hamaker\, Pechenik\, and Weigandt. This talk is based on joint work with Anna Weigandt.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Rohini Ramadas (Warwick Mathematics Institute) DTSTART;VALUE=DATE-TIME:20220414T223000Z DTEND;VALUE=DATE-TIME:20220414T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/66 DESCRIPTION:Title: The S_n action on the homology groups of M_{0\,n}-bar\nby Roh ini Ramadas (Warwick Mathematics Institute) as part of SFU NT-AG seminar\n \n\nAbstract\nThe moduli space M_{0\,n}-bar is a compactification of the s pace of configurations of n points on P^1. The symmetric group on n letter s acts on M_{0\,n}-bar\, and thus on its (co-)homology groups. I will intr oduce M_{0\,n}-bar\, its (co-)homology groups\, and the S_n action. This t alk includes joint work with Rob Silversmith.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/66/ END:VEVENT BEGIN:VEVENT SUMMARY:NTAG faculty DTSTART;VALUE=DATE-TIME:20220915T223000Z DTEND;VALUE=DATE-TIME:20220915T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/68 DESCRIPTION:Title: Social event (meet the NTAG faculty)\nby NTAG faculty as part of SFU NT-AG seminar\n\n\nAbstract\nGrad students - come meet the NTAG fa culty. We'll each say a bit about our areas of interest within algebraic g eometry and/or number theory.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Lena Ji (University of Michigan) DTSTART;VALUE=DATE-TIME:20220922T223000Z DTEND;VALUE=DATE-TIME:20220922T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/69 DESCRIPTION:Title: Rationality of conic bundle threefolds over non-closed fields \nby Lena Ji (University of Michigan) as part of SFU NT-AG seminar\n\n\nAb stract\nClemens–Griffiths introduced the classical intermediate Jacobian obstruction to rationality for complex threefolds\, and used it to show i rrationality of the cubic threefold. Recently\, over non-closed fields\, H assett–Tschinkel and Benoist–Wittenberg refined this obstruction using torsors over the intermediate Jacobian. In this talk\, we identify these intermediate Jacobian torsors for conic bundle threefolds\, and we give ap plications to rationality over non-closed fields. This talk is based on jo int work with S. Frei\, S. Sankar\, B. Viray\, and I. Vogt\, and on joint work with M. Ji.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Bruin (Simon Fraser University) DTSTART;VALUE=DATE-TIME:20220929T223000Z DTEND;VALUE=DATE-TIME:20220929T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/70 DESCRIPTION:Title: Twists of the Burkhardt quartic threefold\nby Nils Bruin (Sim on Fraser University) as part of SFU NT-AG seminar\n\n\nAbstract\nA basic example of a family of curves with level structure is the Hesse pencil of elliptic curves:\n\\[x^3+y^3+z^3+ \\lambda xyz = 0\,\\]\nwhich gives a fam ily of elliptic curves with labelled 3-torsion points. The parameter $\\la mbda$ is a parameter on the corresponding moduli space.\n\nThe analogue fo r genus 2 curves is given by the Burkhardt quartic threefold. In this talk \, we will go over some of its interesting geometric properties. In an ari thmetic context\, where one considers a non-algebraically closed base fiel d\, it is also important to consider the different possible\n \nIn 2003\, Hassett constructed a weighted varian t of $\\overline{M_{0\,n}}(\\mathbb{R})$: For each of the $n$ labels\, we assign a weight between 0 and 1\; points can coincide if the sum of their weights does not exceed one. We seek combinatorial presentations for the f undamental groups of Hassett spaces with certain restrictions on the weigh ts. \n In particular\, we express the Hassett space as a blow-down of $\\overline{M_{0\,n}}$ and modify the cactus group to produce an analog ous short exact sequence. The relations of this modified cactus group invo lves extensions to the braid relations in $S_n$. To establish the sufficie ncy of such relations\, we consider a certain cell decomposition of these Hassett spaces\, which are indexed by ordered planar trees.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/110/ END:VEVENT BEGIN:VEVENT SUMMARY:TBD DTSTART;VALUE=DATE-TIME:20240307T233000Z DTEND;VALUE=DATE-TIME:20240308T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/111 DESCRIPTION:by TBD as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Farbod Shokrieh (University of Washington) DTSTART;VALUE=DATE-TIME:20240314T223000Z DTEND;VALUE=DATE-TIME:20240314T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/112 DESCRIPTION:Title: Heights\, abelian varieties\, and tropical geometry\nby Farb od Shokrieh (University of Washington) as part of SFU NT-AG seminar\n\n\nA bstract\nI will describe some connections between arithmetic geometry of a belian varieties\, non-archimedean/tropical geometry\, and combinatorics. For a principally polarized abelian variety\, we show an identity relating the Faltings height and the Néron--Tate height (of a symmetric effective divisor defining the polarization) which involves invariants arising from non-archimedean/tropical geometry. If time permits\, we also give formula s for (non archimedean) canonical local heights in terms of tropical invar iants. (Based on joint work with Robin de Jong)\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Kyle Yip (UBC) DTSTART;VALUE=DATE-TIME:20240321T223000Z DTEND;VALUE=DATE-TIME:20240321T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/113 DESCRIPTION:Title: Diophantine tuples and bipartite Diophantine tuples\nby Kyle Yip (UBC) as part of SFU NT-AG seminar\n\n\nAbstract\nA set of positive i ntegers is called a Diophantine tuple if the product of any two distinct e lements in the set is one less than a square. There is a long history and extensive literature on the study of Diophantine tuples and their generali zations in various settings. In this talk\, we focus on the following gene ralization: for integers $n \\neq 0$ and $k \\ge 3$\, we call a set of pos itive integers a Diophantine tuple with property $D_{k}(n)$ if the product of any two distinct elements is $n$ less than a $k$-th power\, and we den ote $M_k(n)$ be the largest size of a Diophantine tuple with property $D_{ k}(n)$. I will present an improved upper bound on $M_k(n)$ and discuss its bipartite analogue (where we have a pair of sets instead of a single set) . Joint work with Seoyoung Kim and Semin Yoo.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Pijush Pratim Sarmah (SFU) DTSTART;VALUE=DATE-TIME:20240328T223000Z DTEND;VALUE=DATE-TIME:20240328T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/114 DESCRIPTION:Title: Jacobians of Curves in Abelian Surfaces\nby Pijush Pratim Sa rmah (SFU) as part of SFU NT-AG seminar\n\n\nAbstract\nEvery curve has an abelian variety associated to it\, called the Jacobian. Poincaré's total reducibility theorem states that any abelian variety is isogenuous to a pr oduct of simple abelian varieties. We are interested to know this decompos ition for Jacobians of smooth curves in abelian surfaces. Using Kani and R osen's strikingly simple yet powerful theorem that relates subgroups of au tomorphism groups with isogeny relations on Jacobians\, we will decompose Jacobians of certain curves coming from linear systems of polarizations on abelian surfaces and comment on curve coverings.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Stanley Xiao (UNBC) DTSTART;VALUE=DATE-TIME:20240404T223000Z DTEND;VALUE=DATE-TIME:20240404T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/115 DESCRIPTION:Title: On Hilbert's Tenth Problem and a conjecture of Buchi\nby Sta nley Xiao (UNBC) as part of SFU NT-AG seminar\n\n\nAbstract\nIn this talk I will discuss recent work resolving Buchi's problem\, which has implicati ons for Hilbert's Tenth Problem. In particular\, we show that if there is a tuple of five integer squares $(x_1^2\, x_2^2\, x_3^2\, x_4^2\, x_5^2)$ satisfying $x_{i+2}^2 - 2x_{i+1}^2 + x_i^2 = 2$ for $i = 1\,2\,3$\, then t hese must be consecutive squares. By an old result of J.R. Buchi\, this im plies that there is no general algorithm which can decide whether an arbit rary system of diagonal quadratic form equations admits a solution over th e integers.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleonore Faber (University of Graz) DTSTART;VALUE=DATE-TIME:20240222T233000Z DTEND;VALUE=DATE-TIME:20240223T003000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/117 DESCRIPTION:Title: Friezes and resolutions of plane curve singularities\nby Ele onore Faber (University of Graz) as part of SFU NT-AG seminar\n\n\nAbstrac t\nConway-Coxeter friezes are arrays of positive integers satisfying a det erminantal condition\, the so-called diamond rule. Recently\, these combin atorial objects have been of considerable interest in representation theor y\, since they encode cluster combinatorics of type A.\n\nIn this talk I w ill discuss a new connection between Conway-Coxeter friezes and the combin atorics of a resolution of a complex curve singularity: via the beautiful relation between friezes and triangulations of polygons one can relate eac h frieze to the so-called lotus of a curve singularity\, which was introdu ced by Popescu-Pampu. This allows to interprete the entries in the frieze in terms of invariants of the curve singularity\, and on the other hand\, we can see cluster mutations in terms of the desingularization of the curv e. This is joint work with Bernd Schober.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Pranabesh Das (XULA) DTSTART;VALUE=DATE-TIME:20240704T173000Z DTEND;VALUE=DATE-TIME:20240704T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/118 DESCRIPTION:Title: Sum of three consecutive fifth powers in an arithmetic progressi on\nby Pranabesh Das (XULA) as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/118/ END:VEVENT BEGIN:VEVENT SUMMARY:JM Landsberg (Texas A&M) DTSTART;VALUE=DATE-TIME:20240815T223000Z DTEND;VALUE=DATE-TIME:20240815T233000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/119 DESCRIPTION:Title: Spaces of matrices of bounded rank\nby JM Landsberg (Texas A &M) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nA classical problem in linear algebra is to understand what are the linear s ubspaces of the\nspace of $m\\times n$ matrices such that no matrix in the space has full rank. This problem has connections\nto theoretical compute r science\, more precisely complexity theory\, and algebraic geometry. I w ill give\na history\, explain the connection to algebraic geometry (sheave s on projective space satisfying\nvery special properties)\, and recent pr ogress on the classification question. This is joint work\nwith Hang Huang .\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Giesbrecht (Waterloo) DTSTART;VALUE=DATE-TIME:20240725T173000Z DTEND;VALUE=DATE-TIME:20240725T183000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/120 DESCRIPTION:Title: Functional Decomposition of Sparse Polynomials\nby Mark Gies brecht (Waterloo) as part of SFU NT-AG seminar\n\nLecture held in AQ 5004. \n\nAbstract\nWe consider the algorithmic problem of the functional decomp osition of\nsparse polynomials.\n\nFor example\, (very) given a very high degree $(5*2^100)$ and very sparse (7\nterms) polynomial like\n\n $f(x) = x^(5*2^100) + 15*x^(2^102+2^47) + 90*x^(2^101+2^100 + 2^48)\n + 270*x^(2^101 + 3*2^47) + 405*x^(2^100 + 2^49) + 243*x^(5* 2^47) + 1$\n\nw e ask how to quickly determine whether it can be be quickly written as a\n composition of lower degree polynomials such as\n\n$f(x) = g(h(x)) = g o h = (x^5+1) o (x^(2^100)+3x^(2^{47})).$\n\nMathematically\, Erdos (1949)\ , Schinzel(1987)\, and Zannier(2008) have made\nmajor progress in showing that polynomial roots and functional\ndecompositions of sparse polynomials \, remain (fairly) sparse\, unlike\nfactorizations into irreducibels for e xample.\n\nComputationally\, we have had algorithms for functional decompo sition of\ndense polynomials since Barton & Zippel (1976)\, though the fir st\npolynomial-time algorithms did not arrive until Kozen & Landau (1986}) and\na linear-time algorithm by Gathen et al. (1987)\, at least in the `` tame''\ncase\, where the characteristic of the underlying field does not d ivide the\ndegree.\n\nAlgorithms for polynomial decomposition that exploit sparsity have remained\nelusive until now. We demonstrate new algorithms which provide very fast\nsparsity-sensitive solutions to some of these pr oblems. But important open\nalgorithmic problems remain\, including provi ng indecomposibility\, and more\ngeneral sparse functional decomposition. And there is still considerable\nroom to tighten sparsity bounds in the u nderlying mathematics and/or the\nimplied complexities.\n\nThis is ongoing work with Saiyue Liu (UBC) and Daniel S. Roche (USNA).\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Hendrik Süß (Jena) DTSTART;VALUE=DATE-TIME:20240905T204500Z DTEND;VALUE=DATE-TIME:20240905T214500Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/121 DESCRIPTION:Title: Local volumes of singularities and an algebraic Mahler conjectur e\nby Hendrik Süß (Jena) as part of SFU NT-AG seminar\n\nLecture hel d in K9509.\n\nAbstract\nIn my talk I will discuss the notion of local vol ume for singularities. For the special case of toric singularities this tu rns out to be closely related to the notion of Mahler volume in convex geo metry. This opens a connection between algebraic geometry and unsolved que stions around the Mahler volume. In particular\, I will discuss possible a lgebraic interpretations of the well-known Mahler conjecture.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Shubhodip Mondal (UBC) DTSTART;VALUE=DATE-TIME:20240912T203000Z DTEND;VALUE=DATE-TIME:20240912T213000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/122 DESCRIPTION:Title: Dieudonné theory via cohomology of classifying stacks\nby S hubhodip Mondal (UBC) as part of SFU NT-AG seminar\n\nLecture held in K950 9.\n\nAbstract\nClassically\, Dieudonné theory offers a linear algebraic classification of finite group schemes and p-divisible groups over a perfe ct field of characteristic p>0. In this talk\, I will discuss generalizati ons of this story from the perspective of p-adic cohomology theory (such a s crystalline cohomology\, and the newly developed prismatic cohomology du e to Bhatt--Scholze) of classifying stacks.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Villagra Torcomian (SFU) DTSTART;VALUE=DATE-TIME:20240919T203000Z DTEND;VALUE=DATE-TIME:20240919T213000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/123 DESCRIPTION:Title: Perfect powers as sum of consecutive powers\nby Lucas Villag ra Torcomian (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\ n\nAbstract\nIn 1770 Euler observed that $3^3+4^3+5^3=6^3$ and asked if th ere was another perfect power that equals the sum of consecutive cubes. Th is captivated the attention of many important mathematicians\, such as Cun ningham\, Catalan\, Genocchi and Lucas. In the last decade\, the more gene ral equation $$x^k+(x+1)^k \\cdots (x+d)^k=y^n$$ began to be studied. \n\n In this talk we will focus on this equation. We will see some known result s and one of the most used tools to attack this kind of problems.\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Netan Dogra (King's College London) DTSTART;VALUE=DATE-TIME:20240926T203000Z DTEND;VALUE=DATE-TIME:20240926T213000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/124 DESCRIPTION:by Netan Dogra (King's College London) as part of SFU NT-AG se minar\n\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/124/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART;VALUE=DATE-TIME:20241114T213000Z DTEND;VALUE=DATE-TIME:20241114T223000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/125 DESCRIPTION:by No talk (PIMS Colloquium) as part of SFU NT-AG seminar\n\nL ecture held in K9509.\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/125/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART;VALUE=DATE-TIME:20250123T213000Z DTEND;VALUE=DATE-TIME:20250123T223000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/126 DESCRIPTION:by No talk (PIMS Colloquium) as part of SFU NT-AG seminar\n\nL ecture held in K9509.\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/126/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART;VALUE=DATE-TIME:20250227T213000Z DTEND;VALUE=DATE-TIME:20250227T223000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/127 DESCRIPTION:by No talk (PIMS Colloquium) as part of SFU NT-AG seminar\n\nL ecture held in K9509.\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/127/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART;VALUE=DATE-TIME:20250320T203000Z DTEND;VALUE=DATE-TIME:20250320T213000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/128 DESCRIPTION:by No talk (PIMS Colloquium) as part of SFU NT-AG seminar\n\nL ecture held in K9509.\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/128/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART;VALUE=DATE-TIME:20241017T203000Z DTEND;VALUE=DATE-TIME:20241017T213000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/129 DESCRIPTION:by No talk (PIMS Colloquium) as part of SFU NT-AG seminar\n\nL ecture held in K9509.\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Ollivier (UBC) DTSTART;VALUE=DATE-TIME:20241121T213000Z DTEND;VALUE=DATE-TIME:20241121T223000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/130 DESCRIPTION:by Rachel Ollivier (UBC) as part of SFU NT-AG seminar\n\nLectu re held in K9509.\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Gordon (UBC) DTSTART;VALUE=DATE-TIME:20250130T213000Z DTEND;VALUE=DATE-TIME:20250130T223000Z DTSTAMP;VALUE=DATE-TIME:20240910T203722Z UID:SFUQNTAG/131 DESCRIPTION:by Julia Gordon (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/SFUQNTAG/131/ END:VEVENT END:VCALENDAR