Joint work with Markus Kirschmer\, Fabien Narbonne and Damien Robert
\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabien Pazuki (Copenhagen) DTSTART:20200521T170000Z DTEND:20200521T180000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (SFU) DTSTART:20200528T223000Z DTEND:20200528T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Türkü Özlüm Çelik (Leipzig University) DTSTART:20200604T223000Z DTEND:20200604T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jake Levinson (University of Washington) DTSTART:20200611T223000Z DTEND:20200611T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Avinash Kulkarni (Darmouth) DTSTART:20200625T223000Z DTEND:20200625T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Turchetti (Dalhousie) DTSTART:20200702T223000Z DTEND:20200702T233000Z DTSTAMP:20260404T095902Z 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 of u niversal Mumford curves\, analytic spaces that parametrize both archim edean and non-archimedean uniformizable curves of a fixed genus.\nThis res ult relies on the existence of suitable moduli spaces for marked Schottky groups\, that can be built using the theory of Berkovich spaces over rings of integers of number fields due to Poineau.\nAfter 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://stable.researchseminars.org/talk/SFUQNTAG/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Várilly-Alvarado (Rice University) DTSTART:20200709T223000Z DTEND:20200709T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Bianca Viray (University of Washington) DTSTART:20200716T223000Z DTEND:20200716T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Brendan Creutz (University of Canterbury) DTSTART:20200723T223000Z DTEND:20200723T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosa Winter (MPI MiS) DTSTART:20201029T163000Z DTEND:20201029T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Enis Kaya (University of Groningen) DTSTART:20201105T173000Z DTEND:20201105T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Elisa Lorenzo García (Universtiy of Rennes 1) DTSTART:20201112T173000Z DTEND:20201112T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Sertöz (Max Planck Institute for Mathematics) DTSTART:20201126T173000Z DTEND:20201126T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Monagan (Simon Fraser University) DTSTART:20201119T173000Z DTEND:20201119T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Marseglia (Utrecht University) DTSTART:20201203T173000Z DTEND:20201203T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Agostini (MPI MiS) DTSTART:20201210T173000Z DTEND:20201210T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeline Brandt (Brown University) DTSTART:20210121T173000Z DTEND:20210121T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Anwesh Ray (University of British Columbia) DTSTART:20210128T173000Z DTEND:20210128T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Heaton (The Fields Institute) DTSTART:20210225T173000Z DTEND:20210225T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Fanelli DTSTART:20210204T173000Z DTEND:20210204T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Elina Robeva (University of British Columbia) DTSTART:20210415T163000Z DTEND:20210415T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Lian Duan (Colorado State University) DTSTART:20210408T163000Z DTEND:20210408T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Alp Bassa (Boğaziçi University) DTSTART:20210304T173000Z DTEND:20210304T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Asher Auel (Dartmouth College) DTSTART:20210318T163000Z DTEND:20210318T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Ari Shnidman (Hebrew University of Jerusalem) DTSTART:20210325T163000Z DTEND:20210325T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Fevola (MPI MiS) DTSTART:20210311T173000Z DTEND:20210311T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Tristan Vaccon (Université de Limoges) DTSTART:20210401T163000Z DTEND:20210401T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Özlem Ejder (Boğaziçi University) DTSTART:20210527T163000Z DTEND:20210527T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Lara Bossinger (Instituto de Matemáticas UNAM) DTSTART:20210610T163000Z DTEND:20210610T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Soumya Sankar (Ohio State University) DTSTART:20210708T163000Z DTEND:20210708T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Mateusz Michałek (University of Konstanz) DTSTART:20210624T163000Z DTEND:20210624T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Melissa Sherman-Bennett (UC Berkeley) DTSTART:20210715T163000Z DTEND:20210715T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Selvi Kara (University of South Alabama) DTSTART:20210617T163000Z DTEND:20210617T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Yairon Cid-Ruiz (Ghent University) DTSTART:20210722T163000Z DTEND:20210722T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Anwesh Ray (University of British Columbia) DTSTART:20210729T163000Z DTEND:20210729T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Gillespie (Colorado State University) DTSTART:20210812T163000Z DTEND:20210812T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Vance Blankers (Northeastern University) DTSTART:20210916T163000Z DTEND:20210916T173000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Raymond Cheng (Columbia University) DTSTART:20211028T223000Z DTEND:20211028T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Shabnam Akhtari (University of Oregon) DTSTART:20211118T233000Z DTEND:20211119T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Escobar (Washington University in St. Louis) DTSTART:20211104T223000Z DTEND:20211104T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Habiba Kadiri (University of Lethbridge) DTSTART:20211021T223000Z DTEND:20211021T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabel Vogt (Brown University) DTSTART:20211209T233000Z DTEND:20211210T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Padmavathi Srinivasan (University of Georgia) DTSTART:20211202T233000Z DTEND:20211203T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (Simon Fraser University) DTSTART:20210923T223000Z DTEND:20210923T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ng (University of Lethbridge) DTSTART:20211007T223000Z DTEND:20211007T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Klevdal (University of Utah) DTSTART:20211014T223000Z DTEND:20211014T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricia Klein (University of Minnesota) DTSTART:20220113T233000Z DTEND:20220114T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/53/ END:VEVENT BEGIN:VEVENT SUMMARY:José González (University of California\, Riverside) DTSTART:20220203T233000Z DTEND:20220204T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Bryan (University of British Columbia) DTSTART:20220210T233000Z DTEND:20220211T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Katrina Honigs (Simon Fraser University) DTSTART:20220217T233000Z DTEND:20220218T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Juliette Bruce (University of California\, Berkeley) DTSTART:20220303T233000Z DTEND:20220304T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Pietromonaco (University of British Columbia) DTSTART:20220324T223000Z DTEND:20220324T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Masahiro Nakahara (University of Washington) DTSTART:20220317T223000Z DTEND:20220317T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Marni Mishna (Simon Fraser University) DTSTART:20220331T223000Z DTEND:20220331T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricia Klein (University of Minnesota) DTSTART:20220407T223000Z DTEND:20220407T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Rohini Ramadas (Warwick Mathematics Institute) DTSTART:20220414T223000Z DTEND:20220414T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/66/ END:VEVENT BEGIN:VEVENT SUMMARY:NTAG faculty DTSTART:20220915T223000Z DTEND:20220915T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Lena Ji (University of Michigan) DTSTART:20220922T223000Z DTEND:20220922T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Bruin (Simon Fraser University) DTSTART:20220929T223000Z DTEND:20220929T233000Z DTSTAMP:20260404T095902Z 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 twists of the space. We will discuss an interesting link with a so-called f ield of definition obstruction that occurs for genus 2 curves\, and s ee that this obstruction has interesting consequences for the existence of rational points on certain twists of the Burkhardt quartic.\n\nThis talk is based on joint works with my students Brett Nasserden and Eugene Filato v.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Nahid Walji (University of British Columbia) DTSTART:20221006T230000Z DTEND:20221007T000000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/71 DESCRIPTION:Title: Distribution of traces of Frobenius and the Lang-Trotter conjectu re on average for families of elliptic curves\nby Nahid Walji (Univers ity of British Columbia) as part of SFU NT-AG seminar\n\nLecture held in K -9509.\n\nAbstract\nIn this talk I will discuss distribution results for t races of Frobenius for various families of elliptic curves with respect to the Lang--Trotter conjecture and extremal primes. These are related to th e work of Sha--Shparlinski on the average Lang--Trotter conjecture for sin gle-parametric families as well as the work of various authors on the dist ribution of traces of Frobenius for primes in congruence classes. This is joint work with my former student Nathan Fugleberg.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhe Xu (Simon Fraser University) DTSTART:20221013T223000Z DTEND:20221013T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/72 DESCRIPTION:Title: On the local behaviour of symmetric differentials on the blow-up of Du Val singularities\nby Zhe Xu (Simon Fraser University) as part o f SFU NT-AG seminar\n\nLecture held in K-9509.\n\nAbstract\nDu Val singula rities appear in the classification of algebraic surfaces and other areas of algebraic geometry. Wahl's concept of local Euler characteristics of sh eaves helps in describing the properties of these singularities. We consid er the sheaf of symmetric differentials and compute one ingredient of the local Euler characteristic: the codimension of those symmetric differentia ls that extend to the blow-up of the singularity in the space of those tha t are regular around it. For singularities of type \\(A_n\\)\, we show tha t this codimension can be expressed combinatorially as a lattice point cou nt in a polytope. Ehrhart's quasi-polynomials allow us to find closed expr essions for this codimension as a function of the symmetric differential d egree. We expect our method to generalize to all Du Val singularities.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Kristin DeVleming (University of Massachusetts\, Amherst) DTSTART:20221020T223000Z DTEND:20221020T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/73 DESCRIPTION:Title: A question of Mori and families of plane curves\nby Kristin D eVleming (University of Massachusetts\, Amherst) as part of SFU NT-AG semi nar\n\n\nAbstract\nConsider a smooth family of hypersurfaces of degree d i n P^{n+1}. An old question of Mori is: when is every smooth limit of this family also a hypersurface? While it is easy to construct examples where the answer is "no" when the degree d is composite\, there are no known exa mples when d is prime and n>2! We will pose this as a conjecture (primali ty of degree is sufficient to ensure every smooth limit is a hypersurface\ , for n > 2). However\, there are counterexamples when n=1 or 2. In this t alk\, we will propose a re-formulation of the conjecture that explains the failure in low dimensions\, provide results in dimension one\, and discus s a general approach to the problem using moduli spaces of pairs. This is joint work with David Stapleton.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Brooke (University of Oregon) DTSTART:20221027T223000Z DTEND:20221027T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/74 DESCRIPTION:Title: Abelian surface fibrations and lines on cubic fourfolds\nby C orey Brooke (University of Oregon) as part of SFU NT-AG seminar\n\n\nAbstr act\nIf X is a cubic fourfold (i.e. a hypersurface of degree three in P^5) \, then its Fano variety of lines F is an irreducible symplectic variety o f dimension four. Over the complex numbers\, tools from hyperkähler geome try reveal that F only admits a nontrivial morphism to a lower-dimensional variety when X contains certain "special" algebraic surfaces. In this tal k\, we consider the case when X contains a plane: it turns out that F is b irational to another irreducible symplectic variety admitting a morphism t o P^2 whose general fiber is an abelian surface. We will show the key geom etric ingredients involved in this construction and describe some of its a rithmetic when the ground field is not closed.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Catherine Cannizzo (University of California\, Riverside) DTSTART:20221103T223000Z DTEND:20221103T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/75 DESCRIPTION:Title: Homological Mirror Symmetry for Theta Divisors\nby Catherine Cannizzo (University of California\, Riverside) as part of SFU NT-AG semin ar\n\n\nAbstract\nMirror symmetry relates complex and symplectic manifolds which come in mirror pairs\, and homological mirror symmetry is an equiva lence of categories on each. In forthcoming joint work with Haniya Azam\, Heather Lee\, and Chiu-Chu Melissa Liu\, we prove a global homological mir ror symmetry result for genus 2 curves. We consider genus 2 curves as hype rsurfaces of principally polarized abelian surfaces\, on the complex side. In a follow-up paper\, we allow the abelian variety to have arbitrary dim ension\, and hypersurfaces are now theta divisors. This talk will overview the results of these papers.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Topaz (University of Alberta) DTSTART:20221110T233000Z DTEND:20221111T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/76 DESCRIPTION:Title: An overview of the liquid tensor experiment\nby Adam Topaz (U niversity of Alberta) as part of SFU NT-AG seminar\n\nLecture held in K-95 09.\n\nAbstract\nIn December 2020\, Peter Scholze proposed a challenge to formally verify a theorem he and Dustin Clausen proved about the real numb ers in the context of condensed mathematics\, saying it might be his "most important theorem to date." I was part of the group who took on this chal lenge\, using the Lean3 interactive theorem prover and its formally verifi ed mathematics library `mathlib`. We completed the challenge in July 2022. In this talk\, I will give a broad overview of condensed/liquid mathemati cs and the corresponding formalization in Lean. No background in condensed mathematics or interactive theorem provers will be necessary for this tal k.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Imin Chen (Simon Fraser University) DTSTART:20221117T233000Z DTEND:20221118T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/77 DESCRIPTION:Title: A multi-Frey approach to Fermat equations of signature (11\,11\,n )\nby Imin Chen (Simon Fraser University) as part of SFU NT-AG seminar \n\nLecture held in K-9509.\n\nAbstract\nI will report on joint work with Billerey\, Dieulefait\, Freitas\, and Najman in which we develop some of t he necessary ingredients to use Frey abelian varieties in the modular meth od\, inspired by ideas from Darmon's program for resolving generalized Fer mat equations. In particular\, I will explain how this machinery can be ap plied to study the equation x^11 + y^11 = z^n for first case solutions by using information from multiple Frey varieties.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Tyler Kelly (University of Birmingham) DTSTART:20221124T233000Z DTEND:20221125T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/78 DESCRIPTION:Title: Open Mirror Symmetry for Landau-Ginzburg models\nby Tyler Kel ly (University of Birmingham) as part of SFU NT-AG seminar\n\nLecture held in K-9509.\n\nAbstract\nA Landau-Ginzburg (LG) model is a triplet of data (X\, W\, G) consisting of a regular function $W:X\\to\\mathbb{C}$ from a quasi-projective variety $X$ with a group $G$ acting on $X$ leaving $W$ in variant. One can build an analogue of Hodge theory and period integrals as sociated to an LG model when $G$ is trivial. This involves oscillatory int egrals on certain cycles in\n$X$ (fear not: this is actually cute and will be done in examples!). Mirror symmetry states that period integrals often encode enumerative geometry and this is also the case here. An\nenumerati ve theory developed by Fan\, Jarvis\, and Ruan gives FJRW invariants\, the analogue of Gromov-Witten invariants for LG models. These invariants are now called FJRW invariants. A problem is that finding the right deformatio n period integrals is hard. We define and use a new open enumerative theor y for certain Landau-Ginzburg LG models to solve this problem in low dimen sion. \n\nRoughly speaking\, this involves computing specific integrals on certain moduli of disks with boundary and interior marked points. One can then construct a mirror Landau-Ginzburg model to a Landau-Ginzburg model using these invariants that gives you the right deformation for free. This allows us to prove a mirror symmetry result analogous to that established by Cho-Oh\, Fukaya-Oh-Ohta-Ono\, and Gross for mirror symmetry for toric Fano manifolds. This is joint work with Mark Gross and Ran Tessler.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Yixin Chen (Simon Fraser University) DTSTART:20221201T233000Z DTEND:20221202T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/79 DESCRIPTION:Title: Two-torsion of the Brauer Group of an Elliptic Surface\nby Yi xin Chen (Simon Fraser University) as part of SFU NT-AG seminar\n\nLecture held in K-9509.\n\nAbstract\nThe Brauer group of a variety encodes import ant arithmetic information. For instance\, it plays an important role in t he Brauer-Manin obstruction\, which governs the existence of rational poin ts on many varieties. In this thesis we describe the 2-torsion part of the Brauer group of certain elliptic surfaces. In particular\, we compute exp licit representatives of these elements in terms of quaternion algebras ov er the function field of the surface.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Sho Tanimoto (Nagoya University) DTSTART:20221206T233000Z DTEND:20221207T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/80 DESCRIPTION:Title: From exceptional sets to non-free sections\nby Sho Tanimoto ( Nagoya University) as part of SFU NT-AG seminar\n\nLecture held in K-9509. \n\nAbstract\nManin’s conjecture is a conjectural asymptotic formula for the counting function of rational points on Fano varieties over global fi elds. Mainly with Brian Lehmann\, I have been studying exceptional sets ar ising in this conjecture. In this talk I would like to discuss my joint wo rk with Brian Lehmann and Akash Sengupta on birational geometry of excepti onal sets\, then I will discuss applications of this study to understand t he geometry of moduli spaces of sections on Fano fibrations which is joint work with Brian Lehmann and Eric Riedl.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Catherine Hsu (Swarthmore College) DTSTART:20230216T233000Z DTEND:20230217T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/81 DESCRIPTION:Title: Explicit non-Gorenstein R=T via rank bounds\nby Catherine Hsu (Swarthmore College) as part of SFU NT-AG seminar\n\nLecture held in K-95 09.\n\nAbstract\nIn his seminal work on modular curves and the Eisenstein ideal\, Mazur studied the existence of congruences between certain Eisenst ein series and newforms\, proving that Eisenstein ideals associated to wei ght 2 cusp forms of prime level are locally principal. In this talk\, we'l l explore generalizations of Mazur's result to squarefree level\, focusing on recent work\, joint with P. Wake and C. Wang-Erickson\, about a non-op timal level N that is the product of two distinct primes and where the Gal ois deformation ring is not expected to be Gorenstein. First\, we will out line a Galois-theoretic criterion for the deformation ring to be as small as possible\, and when this criterion is satisfied\, deduce an R=T theorem . Then we'll discuss some of the techniques required to computationally ve rify the criterion.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/81/ END:VEVENT BEGIN:VEVENT SUMMARY:June Park (University of Melbourne) DTSTART:20230126T233000Z DTEND:20230127T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/82 DESCRIPTION:Title: Space of morphisms & Moduli stack of elliptic fibrations\nby June Park (University of Melbourne) as part of SFU NT-AG seminar\n\n\nAbst ract\nThe defining property of fine moduli stacks (of curves) is that they have 'universal families' which translates the study of a family of (curv es) as the study of morphisms to moduli stacks. I will explain this idea u sing Hom_{n}(P^1\, Mbar_{1\,1}) the space of rational curves on the moduli stack of stable elliptic curves. Once we have the space\, we will compute some arithmetic invariants via topological methods.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/82/ END:VEVENT BEGIN:VEVENT SUMMARY:(reading break) DTSTART:20230223T233000Z DTEND:20230224T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/83 DESCRIPTION:by (reading break) as part of SFU NT-AG seminar\n\nAbstract: T BA\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Inchiostro (University of Washington) DTSTART:20230323T223000Z DTEND:20230323T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/84 DESCRIPTION:Title: Wall crossing morphisms for moduli of stable pairs\nby Giovan ni Inchiostro (University of Washington) as part of SFU NT-AG seminar\n\nL ecture held in AQ 4140.\n\nAbstract\nConsider a quasi-compact moduli space M of pairs (X\,D) consisting of a variety X and a divisor D on X. If M is not proper\, it is reasonable to find a compactification of it. Assume fu rthermore that there are two rational numbers $0 \\lt b \\lt a\\lt 1$ such that\, for every pair (X\,D) corresponding to a point in M\, the pair (X\ ,D) is smooth and normal crossings\, and the Q-divisors $K_X+aD$ and $K_X+ bD$ are ample. Using Kollár's formalism of stable pairs\, one can constru ct two different compactifications of M (M_a and M_b)\, corresponding to a and b. I will explain how to relate these two compactifications. The main result is that\, up to replacing M_a and M_b with their normalizations\, there are birational morphisms $M_a \\to M_b$\, recovering Hassett's resul t (for the case of curves) in all dimensions. If time permits\, I will exp lain a slight variation of the moduli functor of varieties with pairs\, wh ich has a particularly accessible moduli functor\, leads to a simple proof of the projectivity of the moduli of stable pairs\, and conjecturally lea ds to better wall-crossing phenomena. The talk will be based on my work wi th Kenny Ascher\, Dori Bejleri\, Zsolt Patakfalvi\; and my work with Stefa no Filipazzi.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Jen Paulhus (Grinnell College) DTSTART:20230330T223000Z DTEND:20230330T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/85 DESCRIPTION:Title: (postponed) Automorphism groups of Riemann surfaces\nby Jen P aulhus (Grinnell College) as part of SFU NT-AG seminar\n\nLecture held in K-9509.\n\nAbstract\n(postponed)\n\nA well-known result on compact Riemann surfaces says that the automorphism group of any such surface is a finite group of bounded size (based on the genus of the surface). Additionally\ , the Riemann-Hurwitz formula gives us an expectation for when a particula r group should be the automorphism group of a Riemann surface of a particu lar genus. There has been a lot of work over the last 20 years to classify which groups show up for a given genus. \n\nThis talk will introduce the core ideas in the field\, explain the connection with curves over number f ields\, and talk about recent results to classify groups which are indeed automorphisms in just about every genus they should be. We’ll also make a surprising connection to simple groups.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Ahmad Mokhtar (Simon Fraser University) DTSTART:20230202T233000Z DTEND:20230203T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/86 DESCRIPTION:Title: Fano schemes of singular symmetric matrices\nby Ahmad Mokhtar (Simon Fraser University) as part of SFU NT-AG seminar\n\nLecture held in K-9509.\n\nAbstract\nFano schemes are moduli spaces that parameterize lin ear spaces contained in an embedded projective variety. In this talk\, I i nvestigate the Fano schemes parameterizing linear subspaces of symmetric m atrices whose elements are all singular. I discuss their irreducibility\, smoothness\, and connectedness and show that they can have generically non -reduced components. As an application\, I outline how to use the geometry of these schemes to give alternative arguments for several results on sub spaces of singular symmetric matrices.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Eva-Marie Hainzl (TU Wien) DTSTART:20230209T233000Z DTEND:20230210T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/87 DESCRIPTION:Title: Universal types of singularities of solutions to functional equat ion systems\nby Eva-Marie Hainzl (TU Wien) as part of SFU NT-AG semina r\n\nLecture held in K-9509.\n\nAbstract\nDecompositions of combinatorial structures translate very often to functional equations with positive coef ficients for their generating functions. A theorem by Bender says that if the generating function is univariate and the equation not linear\, the ge nerating function always has a dominant square root singularity - which in turn means that the the coefficients a(n) grow asymptotically at the rate c*n^(-3/2) R^n\, where c and R are suitable constants. The result extends to strongly connected finite systems of equations\, but as the system bec omes infinite we can observe a broader variety of singularities appearing. \nIn this talk\, I will give an overview of functional equations systems and their singular behaviour in combinatorics and present some recent resu lts on universal types of singularities of solutions to infinite systems w hich collapse to a single equation by introducing a second (catalytic) var iable.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Yifeng Huang (University of British Columbia) DTSTART:20230302T233000Z DTEND:20230303T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/88 DESCRIPTION:Title: Matrix points on varieties and punctual Hilbert (and Quot) scheme s\nby Yifeng Huang (University of British Columbia) as part of SFU NT- AG seminar\n\nLecture held in K-95095.\n\nAbstract\nModuli spaces often ha ve interesting enumerative properties. The goal of this talk is to introdu ce some enumerative results on solutions of matrix equations and zero-dime nsional sheaves over singular curves. To motivate them\, I first discuss s everal moduli spaces in general\, which I put onto the "unframed" side and the "framed" side. The unframed side includes the commuting variety AB=BA of n x n matrices\, the variety of commuting matrices satisfying polynomi al equations (the titular "matrix points on varieties")\, and the moduli s tack of zero-dimensional coherent sheaves on a variety. The framed side in cludes the Hilbert scheme of points on a variety\, or more generally\, the Quot scheme of zero-dimensional quotients of a vector bundle on a variety . The enumerative properties to be considered are point counts over finite fields and the motive in the Grothendieck ring of varieties\, which essen tially keep track of the combinatorial data of a stratification of the spa ce in question. I will explain some general connections within and between the two sides\, and known results for smooth curves and smooth surfaces. Finally\, I will discuss recent results on singular curves. This talk is b ased on joint work with Ruofan Jiang.\n\nIn the pre-seminar\, I plan to ta lk about a super fun combinatorial construction\, which we call “spiral shifting operators”\, used in the proof of one of our results.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Sharon Robins (Simon Fraser University) DTSTART:20230309T233000Z DTEND:20230310T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/89 DESCRIPTION:Title: Deformations of Smooth Projective Toric Varieties\nby Sharon Robins (Simon Fraser University) as part of SFU NT-AG seminar\n\nLecture h eld in K-9509.\n\nAbstract\nWe can study how a given scheme X fits into a family using the tools from the deformation theory. One begins by using in finitesimal methods\, studying possible obstructions\, and attempting to c onstruct a family called a versal deformation\, which collects all possibl e deformations. If X is a smooth projective toric variety\, combinatorial descriptions of the space of first-order deformations and the obstruction to second-order deformation given by the cup product have been studied. In this talk\, I will present these descriptions with an example of a smooth projective toric threefold with a quadratic obstruction. In addition\, I will discuss my current research\, which provides a combinatorial iterativ e procedure for finding higher-order obstructions.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Susan Cooper (University of Manitoba) DTSTART:20230317T223000Z DTEND:20230317T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/90 DESCRIPTION:Title: Limiting Behaviour of Symbolic Powers\nby Susan Cooper (Unive rsity of Manitoba) as part of SFU NT-AG seminar\n\nLecture held in AQ 4120 .\n\nAbstract\nAt the heart of many problems in Commutative Algebra and Al gebraic Geometry is the difference between symbolic and regular powers of a homogeneous ideal. One way to find failures of containments between thes e powers is to use an asymptotic approach and look at a special limit call ed the Waldschmidt constant. This limit was first introduced as a way to e stimate the lowest degree of a hypersurface vanishing at all the points of a variety to a given order. However\, this limit is challenging to comput e and so it is natural to focus our attention on special ideals to gain in sight. In this talk we will give some interpretations of the Waldschmidt constant of a monomial ideal which allow us to determine this limit in a n umber of cases. This is joint work from two projects: the first with R. Em bree\, H. T. Hà\, and A. Hoefel and the second with C. Bocci\, E. Guardo\ , B. Harbourne\, M. Janssen\, U. Nagel\, A. Seceleanu\, A. Van Tuyl\, and T. Vu.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandru Constantinescu (Freie Universität Berlin) DTSTART:20230331T223000Z DTEND:20230331T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/91 DESCRIPTION:Title: Cotangent Cohomology for Matroids\nby Alexandru Constantinesc u (Freie Universität Berlin) as part of SFU NT-AG seminar\n\nLecture held in 3:30-4:20.\n\nAbstract\nThe first cotangent cohomology module $T^1$ de scribes the first order deformations of a commutative ring. For Stanley-Re isner rings\, this module has a purely combinatorial description: its mult igraded components are given as the relative cohomology of some topologica l spaces associated to the defining simplicial complex. When the Stanley-R eisner ring is associated to a matroid\, I will present a very explicit fo rmula for the dimensions of these components. Furthermore\, I will show th at $T^1$ provides a new complete characterization for matroids.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Katz (California State University\, Northridge) DTSTART:20230809T173000Z DTEND:20230809T183000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/92 DESCRIPTION:Title: Rationality of four-valued families of binomial Weil sums\nby Daniel Katz (California State University\, Northridge) as part of SFU NT- AG seminar\n\nLecture held in K9509.\n\nAbstract\nConsider the Weil sum $W _{F\,d}(a)=\\sum_{x \\in F} \\psi(x^d-a x)$\, where \n$F$ is a finite fiel d\, $\\psi$ is the canonical additive character of \n$F$\, the coefficient $a$ is a nonzero element of $F$\, and $d$ is a \npositive integer such th at $\\gcd(d\,|F|-1)=1$. This last condition makes \n$x\\mapsto x^d$ a pow er permutation of $F$\, that is\, a power map that \npermutes $F$. These Weil sums include Kloosterman sums as the special \ncase when one sets $d= |F|-2$ and deducts $1$ from the Weil sum to obtain \nthe Kloosterman sum. The Weil spectrum for $F$ and $d$ records the \nvalues $W_{F\,d}(a)$ as $ a$ runs through $F^*$. Weil sums in which the \nargument of the character is a binomial of the form $x^d-a x$ are used \nto count points on varieti es over finite fields\, and have multiple \napplications to cryptography a nd communications. Since one sums roots \nof unity in the complex plane t o obtain the Weil spectrum values\, these \nare always algebraic integers. A rational Weil spectrum is one whose \nvalues are all rational integers . If one sets aside degenerate cases\, \nHelleseth showed that Weil spect ra have at least three distinct values. \nIt has been shown that all spect ra with exactly three distinct values \nare rational. In this talk\, we s how that\, with one exception\, Weil \nspectra with exactly four distinct values are also always rational. \nThis is joint work with Allison E.\\ Wo ng\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/92/ END:VEVENT BEGIN:VEVENT SUMMARY:All NTAG faculty and students DTSTART:20230907T223000Z DTEND:20230907T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/93 DESCRIPTION:Title: How to NTAG...get the most out of the seminar!\nby All NTAG f aculty and students as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Zotine (Queen's University) DTSTART:20230914T223000Z DTEND:20230914T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/94 DESCRIPTION:Title: Computing Higher Direct Images of Toric Morphisms\nby Alexand re Zotine (Queen's University) as part of SFU NT-AG seminar\n\n\nAbstract\ nSheaf cohomology is a ubiquituous tool in algebraic geometry for understa nding the structure of varieties---but how does one actually get one's han ds on cohomology? In this talk\, I will discuss computing sheaf cohomology (and higher direct images) of toric varieties\, which translate geometry into combinatorics. This translation is far more accessible and amenable t o computation\, allowing us to get a more tangible grasp of the abstract c onstructions. In particular\, I implemented an algorithm for computing the higher direct images of toric morphisms for line bundles in Macaulay2\, w hich I will demonstrate. This is joint work with Mike Roth and Greg Smith. \n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Shoemaker (Colorado State) DTSTART:20231130T233000Z DTEND:20231201T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/95 DESCRIPTION:Title: Counting curves in quiver varieties\nby Mark Shoemaker (Color ado State) as part of SFU NT-AG seminar\n\n\nAbstract\nFrom a directed gra ph $Q$\, called a quiver\, one can construct what is known as a quiver var iety $Y_Q$\, an algebraic variety defined as a quotient of a vector space by a group defined in terms of $Q$. A mutation of a quiver is an operatio n that produces from $Q$ a new directed graph $Q’$ and a new associated quiver variety $Y_{Q’}$. Quivers and mutations have a number of connect ions to representation theory\, combinatorics\, and physics. The mutation conjecture predicts a surprising and beautiful connection between the num ber of curves in $Y_Q$ and the number in $Y_{Q’}$. In this talk I will describe quiver varieties and mutations\, give some examples to convince y ou that you’re already well-acquainted with some quiver varieties and th eir mutations\, and discuss an application to the study of determinantal v arieties. This is based on joint work with Nathan Priddis and Yaoxiong We n.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Jen Paulhus (Grinnell College) DTSTART:20231012T223000Z DTEND:20231012T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/96 DESCRIPTION:Title: Automorphism groups of Riemann surfaces\nby Jen Paulhus (Grin nell College) as part of SFU NT-AG seminar\n\n\nAbstract\nA well-known res ult on compact Riemann surfaces says that the automorphism group of any su ch surface is a finite group of bounded size (based on the genus of the su rface). Additionally\, the Riemann-Hurwitz formula gives us an expectation for when a particular group should be the automorphism group of a Riemann surface of a particular genus. There has been a lot of work over the last 20 years to classify which groups show up for a given genus. \n \nThis ta lk will introduce the core ideas in the field\, explain the connection wit h curves over number fields\, and talk about recent results to classify gr oups which are indeed automorphisms in just about every genus they should be. We’ll also make a surprising connection to simple groups.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Ursula Whitcher (AMS) DTSTART:20231123T233000Z DTEND:20231124T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/97 DESCRIPTION:Title: Adinkra heights and color-splitting rainbows\nby Ursula Whitc her (AMS) as part of SFU NT-AG seminar\n\n\nAbstract\nAdinkras are decorat ed graphs that encapsulate information about conjectural relationships bet ween fundamental particles in physics. If we color the edges of an Adinkra with a rainbow of shades in a specific order\, we obtain a special curve that we can study using algebraic and geometric techniques. We use this st ructure to characterize height functions on Adinkras with five colors\, th en show how to compute the same information using data from our rainbow. T his talk describes joint work with Amanda Francis.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Emiel Haakma (SFU) DTSTART:20231019T230000Z DTEND:20231020T000000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/98 DESCRIPTION:Title: A method of 2-descent on a genus 3 hyperelliptic curve\nby Em iel Haakma (SFU) as part of SFU NT-AG seminar\n\n\nAbstract\nThe rational points of an abelian variety form a finitely generated group and computin g the rank of this group is a hard and central problem in arithmetic geome try. One method\, which follows the original proof of Mordell and Weil of the finiteness of this rank\, is explicit finite descent. It approximates it using Selmer groups\, which bounds the rank using local information. Th e Tate-Shafarevich group measures the failure of this bound to be sharp. I t is one of the most mysterious objects in arithmetic geometry.\n\nTate-Sh afarevich groups have been shown to grow arbitrarily large in certain fami lies by comparing different but related Selmer groups. Results on this hav e been primarily for Jacobians of hyperelliptic and superelliptic curves\, which have additional automorphisms.\n\nWe discuss generalizations of the se methods to curves of genus 3\, which has the important distinction that not all curves are hyperelliptic. This will give us computational access to various Selmer groups of abelian threefolds with minimal endomorphism r ing and that are not hyperelliptic Jacobians\, and potentially allow us to show that the 2-torsion of Tate-Shafarevich groups for them is unbounded. \n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Jake Levinson (Université de Montréal) DTSTART:20231026T223000Z DTEND:20231026T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/99 DESCRIPTION:Title: Minimal degree fibrations in curves and asymptotic degrees of irr ationality\nby Jake Levinson (Université de Montréal) as part of SFU NT-AG seminar\n\n\nAbstract\nA basic question about an algebraic variety X is how similar it is to projective space. One measure of similarity is t he minimum degree of a rational map from X to projective space\, the "degr ee of irrationality". This number\, not to mention the corresponding minim al-degree maps\, is in general challenging to compute\, but captures speci al features of the geometry of X. I will discuss some recent joint work wi th David Stapleton and Brooke Ullery on asymptotic bounds for degrees of i rrationality of divisors X on projective varieties Y. Here\, the minimal-d egree rational maps $X \\dashrightarrow \\mathbb{P}^n$ turn out to "know" about Y and factor through rational maps $Y \\dashrightarrow \\mathbb{P}^n $ fibered in curves that are\, in an appropriate sense\, also of minimal d egree.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Meazinni (Bologna) DTSTART:20231109T233000Z DTEND:20231110T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/100 DESCRIPTION:Title: On some formality problems in deformation theory\nby Frances co Meazinni (Bologna) as part of SFU NT-AG seminar\n\n\nAbstract\nI will b riefly introduce the notion of formality for differential graded Lie algeb ras\, and the role it plays in deformation theory. I will then discuss som e geometric applications obtained in a joint work with Claudio Onorati.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Petracci (Bologna) DTSTART:20231102T223000Z DTEND:20231102T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/101 DESCRIPTION:Title: Moduli spaces of Fano varieties can be singular\nby Andrea P etracci (Bologna) as part of SFU NT-AG seminar\n\n\nAbstract\nFano varieti es are projective algebraic variety with “positive curvature”. Recentl y\, using the notion of K-stability which originates in differential geome try\, projective moduli spaces for Fano varieties have been constructed. I n this talk I will show how to use polytopes and toric geometry (which is the study of certain algebraic varieties constructed in a combinatorial fa shion) to produce singular points on these moduli spaces of Fano varieties . The talk is based on joint work with Anne-Sophie Kaloghiros.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Bragg (Utah) DTSTART:20231116T233000Z DTEND:20231117T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/102 DESCRIPTION:Title: Murphy's Law for the stack of curves\nby Daniel Bragg (Utah) as part of SFU NT-AG seminar\n\n\nAbstract\nWhen trying to classify curve s over a non-algebraically closed field\, one quickly runs into the diffic ulty that there are curves which are not defined over their fields of modu li. We will explain what this means with some examples. We will discuss ho w this phenomenon can be thought of geometrically in the moduli space of c urves\, using residual gerbes. We will then explain some recent work with Max Lieblich on solving the corresponding inverse problem: specifically\, we show that every Deligne-Mumford gerbe over a field occurs as the residu al gerbe of a point of the moduli stack of curves. This means that every p ossible way that a curve could fail to be defined over its field of moduli actually does occur\, that is\, everything that could go wrong does.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Bruin (SFU) DTSTART:20230928T223000Z DTEND:20230928T233000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/103 DESCRIPTION:Title: Jacobians of genus 4 curves that are (2\,2)-decomposable\nby Nils Bruin (SFU) as part of SFU NT-AG seminar\n\n\nAbstract\nDecomposable abelian varieties\, and particularly decomposable Jacobians\, have a long history\; mainly in the form of formulas to compute hyperelliptic integra ls in terms of elliptic ones.\n\nThe first case where one can have a decom posable Jacobian without elliptic factors is for genus 4: one could have o ne that is isogenous to the product of two genus 2 Jacobians. Interestingl y\, though\, not all four-dimensional abelian varieties (not even the prin cipally polarized ones) are Jacobians. Classifying which genus 2 Jacobians can be glued together to yield a Jacobian of a genus 4 curve leads to som e very interesting geometry on the Castelnuovo-Richmond-Igusa quartic thre efold. We will introduce the requisite geometry and sketch some interestin g results that follow.\n\nThis is joint work with Avinash Kulkarni.\n\nThe re will be an informal pre-seminar for graduate students at 3pm.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/103/ END:VEVENT BEGIN:VEVENT SUMMARY:TBD DTSTART:20240118T233000Z DTEND:20240119T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/105 DESCRIPTION:by TBD as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Debaditya Raychaudhury (University of Arizona) DTSTART:20240125T233000Z DTEND:20240126T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/106 DESCRIPTION:Title: On the singularities of secant varieties\nby Debaditya Raych audhury (University of Arizona) as part of SFU NT-AG seminar\n\n\nAbstract \nIn this talk\, we study the singularities of secant varieties of smooth projective varieties when the embedding line bundle is sufficiently positi ve. We give a necessary and sufficient condition for these to have p-Du Bo is singularities. In addition\, we show that the singularities of these va rieties are never higher rational. From our results\, we deduce several co nsequences\, including a Kodaira-Akizuki-Nakano type vanishing result for the reflexive differential forms of the secant varieties. Work in collabor ation with S. Olano and L. Song.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/106/ END:VEVENT BEGIN:VEVENT SUMMARY:TBD DTSTART:20240201T233000Z DTEND:20240202T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/107 DESCRIPTION:by TBD as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Williams (UBC) DTSTART:20240208T233000Z DTEND:20240209T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/108 DESCRIPTION:Title: Extraordinary involutions on Azumaya algebras\nby Ben Willia ms (UBC) as part of SFU NT-AG seminar\n\n\nAbstract\nThis is joint work wi th Uriya First. If $R$ is a ring and $n$ is a natural number\, then an Azu maya algebra of degree $n$ on $R$ is an $R$-algebra such that $A$ becomes isomorphic to the $n \\times n$ matrix algebra after some faithfully flat extension of scalars. An involution of an Azumaya algebra is an additive s elf map of order $2$ that reverses the multiplication. One obtains example s of Azumaya algebras with involution by starting with a projective $R$-mo dule $P$ of rank $n$\, equipped with a hermitian form. The endomorphism ri ng $\\End_R(P)$ has the structure of an Azumaya algebra with involution. O ne may even allow the hermitian form to take values in a rank-$1$ projecti ve $R$-module\, rather than in $R$ itself.\n\nWe will say that an Azumaya algebra with involution $(A\, \\sigma)$ is semiordinary if there it become s isomorphic to one constructed from a hermitian form after a faithfully f lat extension of scalars. Although this is an extremely broad class of Azu maya algebras with involution\, I will show that it is not all of them: th ere exist Azumaya algebras with truly extraordinary involutions. The metho d is to find an obstruction to being semiordinary in equivariant algebraic topology.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter McDonald (University of Utah) DTSTART:20240215T233000Z DTEND:20240216T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/109 DESCRIPTION:Title: Splinter-type conditions for classifying singularities\nby P eter McDonald (University of Utah) as part of SFU NT-AG seminar\n\n\nAbstr act\nThe Direct Summand Theorem states that if $R$ is a commutative Noethe rian ring\, then any finite extension $R\\to S$ splits as a map of $R$-mod ules. This suggests the notion of a splinter as a class of singularities\, where we say a scheme $X$ is a splinter if\, for any finite surjective ma p $\\pi:Y\\to X$ the natural map $\\mathcal{O}_X\\to\\pi_*\\mathcal{O}_Y$ splits as a map of $\\mathcal{O}_X$-modules. In this talk\, I'll discuss t he history of using splinter-type conditions to classify singularities\, i ncluding work of Bhatt and Kov\\'acs\, with the goal of introducing a rece nt result giving a splinter-type characterization of klt singularities.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Haggai Liu (Simon Fraser University) DTSTART:20240229T233000Z DTEND:20240301T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/110 DESCRIPTION:Title: Moduli Spaces of Weighted Stable Curves and their Fundamental Gr oups\nby Haggai Liu (Simon Fraser University) as part of SFU NT-AG sem inar\n\n\nAbstract\nThe Deligne-Mumford compactification\, $\\overline{M_{ 0\,n}}$\, of the moduli space of $n$ distinct ordered points on $\\mathbb{ P}^1$\, has many well understood geometric and topological properties. For example\, it is a smooth projective variety over its base field. Many int eresting properties are known for the manifold $\\overline{M_{0\,n}}(\\mat hbb{R})$ of real points of this variety. In particular\, its fundamental g roup\, $\\pi_1(\\overline{M_{0\,n}}(\\mathbb{R}))$\, is related\, via a sh ort exact sequence\, to another group known as the cactus group. Henriques and Kamnitzer gave an elegant combinatorial presentation of this cactus g roup.\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://stable.researchseminars.org/talk/SFUQNTAG/110/ END:VEVENT BEGIN:VEVENT SUMMARY:TBD DTSTART:20240307T233000Z DTEND:20240308T003000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/111 DESCRIPTION:by TBD as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Farbod Shokrieh (University of Washington) DTSTART:20240314T223000Z DTEND:20240314T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Kyle Yip (UBC) DTSTART:20240321T223000Z DTEND:20240321T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Pijush Pratim Sarmah (SFU) DTSTART:20240328T223000Z DTEND:20240328T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Stanley Xiao (UNBC) DTSTART:20240404T223000Z DTEND:20240404T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleonore Faber (University of Graz) DTSTART:20240222T233000Z DTEND:20240223T003000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Pranabesh Das (XULA) DTSTART:20240704T173000Z DTEND:20240704T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/118/ END:VEVENT BEGIN:VEVENT SUMMARY:JM Landsberg (Texas A&M) DTSTART:20240815T223000Z DTEND:20240815T233000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Giesbrecht (Waterloo) DTSTART:20240725T173000Z DTEND:20240725T183000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Hendrik Süß (Jena) DTSTART:20240905T204500Z DTEND:20240905T214500Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Shubhodip Mondal (UBC) DTSTART:20240912T203000Z DTEND:20240912T213000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Villagra Torcomian (SFU) DTSTART:20240919T203000Z DTEND:20240919T213000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Netan Dogra (King's College London) DTSTART:20240926T203000Z DTEND:20240926T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/124 DESCRIPTION:Title: Rational points on hyperelliptic curves via nonabelian descent\nby Netan Dogra (King's College London) as part of SFU NT-AG seminar\n\ n\nAbstract\nLet $f(x)$ be a separable polynomial with rational number coe fficients. In this talk I will review how the rational points of the hyper elliptic curve $y^2 = f(x)$ can sometimes be determined using the number f ield obtained by adjoining a root of $f$\, via the Chabauty--Coleman metho d and the theory of the $2$-Selmer group. I will then explain the limitati ons of this method\, and how to give a `nonabelian' generalisation. The pu nchline will be that\, if the Chabauty--Coleman method doesn't work\, we c an sometimes determine the rational points using the field obtained by adj oining two roots of $f$.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/124/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART:20241114T213000Z DTEND:20241114T223000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/125/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART:20250123T213000Z DTEND:20250123T223000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Rahul Dalal (University of Vienna) DTSTART:20250227T203000Z DTEND:20250227T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/127 DESCRIPTION:Title: Automorphic Representations and Quantum Logic Gates (joint semin ar with UBC)\nby Rahul Dalal (University of Vienna) as part of SFU NT- AG seminar\n\n\nAbstract\nAny construction of a quantum computer requires finding a good set\nof universal quantum logic gates: abstractly\, a finit e set of matrices in\nU(2^n) such that short products of them can efficien tly approximate\narbitrary unitary transformations. The 2-qubit case n=2 i s of particular\npractical interest. I will present the first construction of an optimal\,\nso-called "golden" set of 2-qubit gates. \n\nThe modern theory of automorphic representations on unitary groups---in\nparticular\, the endoscopic classification and higher-rank versions of the\nRamanujan bound---will play a crucial role in proving the necessary analytic\nestima te: specifically\, a weight-aspect variant of the density hypothesis\nfirs t considered by Sarnak and Xue.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/127/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART:20241017T203000Z DTEND:20241017T213000Z DTSTAMP:20260404T095902Z 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://stable.researchseminars.org/talk/SFUQNTAG/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Ollivier (UBC) DTSTART:20241121T213000Z DTEND:20241121T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/130 DESCRIPTION:Title: Rigid dualizing complexes for affine Hecke algebras\nby Rach el Ollivier (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n \nAbstract\nGrothendieck's duality theory relies on the notion of a dualiz ing complex. In the non-commutative setting such dualizing complexes were studied in the 90s beginning with work by Yekutieli. Since these complexes are not unique (for example\, one can tensor them with any invertible obj ect) Van der Bergh subsequently introduced the notion of a rigid dualizing complex.\n\nWe will discuss rigid dualizing complexes in the context of ( generic) affine Hecke algebras and see what sort of consequences one can d raw.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Dijols (UBC) DTSTART:20241128T213000Z DTEND:20241128T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/132 DESCRIPTION:Title: Parabolically induced representations of p-adic G2 distinguished by SO4\nby Sarah Dijols (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nDistinguished representations are representat ions of a reductive group $G$ on a vector space $V$ such that there exists a $H$-invariant linear form for a subgroup $H$ of $G$. They intervene in the Plancherel formula in a relative setting\, as well as in the Sakellari dis-Venkatesh conjectures for instance. I will explain how the Geometric L emma allows us to classify parabolically induced representations of the $p $-adic group $G_2$ distinguished by $SO_4$. In particular\, I will describ e a new approach\, in progress\, where we use the structure of the p-adic octonions and their quaternionic subalgebras to describe the double coset space $P\\backslash G_2/SO_4$\, where $P$ stands for the maximal parabolic subgroups of $G_2$.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Tian Wang (Concordia) DTSTART:20250116T213000Z DTEND:20250116T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/133 DESCRIPTION:Title: Effective open image theorem for products of principally polariz ed abelian varieties\nby Tian Wang (Concordia) as part of SFU NT-AG se minar\n\n\nAbstract\nLet $E/\\mathbb{Q}$ be an elliptic curve without comp lex multiplication. By Serre's open image theorem\, the mod $\\ell$ Galois representation $\\overline{\\rho}_{E\, \\ell}$ of $E$ is surjective for e ach prime number $\\ell$ that is sufficiently large. Partially motivated by Serre's uniformity question\, there has been research into an effective version of this result\, which aims to find an upper bound on the largest prime $\\ell$ such that $\\overline{\\rho}_{E\, \\ell}$ is nonsurjective. In this talk\, we consider an analogue of the problem for a product of pr incipally polarized abelian varieties $A_1\, \\ldots\, A_n$ over $K$\, whe re the varieties are pairwise non-isogenous over $\\overline{K}$. We will present an effective version of the open image theorem for $A_1\\times \\ ldots \\times A_n$ due to Hindry and Ratazzi. This is joint work with Jaco b Mayle.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/133/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (OR Seminar) DTSTART:20241205T213000Z DTEND:20241205T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/134 DESCRIPTION:by No talk (OR Seminar) as part of SFU NT-AG seminar\n\nLectur e held in K9509.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Katrina Honigs (SFU) DTSTART:20250410T203000Z DTEND:20250410T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/135 DESCRIPTION:Title: McKay correspondence for reflection groups and derived categorie s\nby Katrina Honigs (SFU) as part of SFU NT-AG seminar\n\nLecture hel d in K9509.\n\nAbstract\nThe classical McKay correspondence shows that the re is a bijection between irreducible representations of finite subgroups $G$ of $\\mathrm{SL}(2\,\\mathbb{C})$ and the exceptional divisors of the minimal resolution of the singularity $\\mathbb{C}^2/G$. This is a very el egant correspondence\, but it's not at all obvious how to extend these ide as to other finite groups.\n\nKapranov and Vasserot\, and then\, later\, B ridgeland\, King and Reid showed this correspondence can be recast and ext ended as an equivalence of derived categories of coherent sheaves. When th is framework is extended to finite subgroups of $\\mathrm{GL}(2\,\\mathbb{ C})$ generated by reflections\, the equivalence of categories becomes a se miorthogonal decomposition whose components are\, conjecturally\, in bijec tion with irreducible representations of $G$. This correspondence has been verified in recent work of Potter and of Capellan for a particular embedd ing of the dihedral groups $D_n$ in $\\mathrm{GL}(2\,\\mathbb{C})$. I will discuss recent joint work verifying this decomposition in further cases.\ n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Seda Albayrak (SFU) DTSTART:20250213T213000Z DTEND:20250213T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/136 DESCRIPTION:Title: Multivariate Generalization of Christol’s Theorem\nby Seda Albayrak (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\n Abstract\nChristol's theorem (1979)\, which sets ground for many interacti ons between theoretical computer science and number theory\, characterizes the coefficients of a formal power series over a finite field of positive characteristic $p>0$ that satisfy an algebraic equation to be the sequenc es that can be generated by finite automata\, that is\, a finite-state mac hine takes the base-$p$ expansion of $n$ for each coefficient and gives th e coefficient itself as output. Namely\, a formal power series $\\sum_{n\ \ge 0} f(n) t^n$ over $\\mathbb{F}_p$ is algebraic over $\\mathbb{F}_p (t) $ if and only if $f(n)$ is a $p$-automatic sequence. However\, this charac terization does not give the full algebraic closure of $\\mathbb{F}_p (t)$ . Later it was shown by Kedlaya (2006) that a description of the complete algebraic closure of $\\mathbb{F}_p (t)$ can be given in terms of $p$-quas i-automatic generalized (Laurent) series. In fact\, the algebraic closure of $\\mathbb{F}_p (t)$ is precisely generalized Laurent series that are $p $-quasi-automatic. We will characterize elements in the algebraic closure of function fields over a field of positive characteristic via finite auto mata in the multivariate setting\, extending Kedlaya's results. In particu lar\, our aim is to give a description of the full algebraic closure for m ultivariate fraction fields of positive characteristic.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Romina M. Arroyo (Universidad Nacional de Cordoba) DTSTART:20250109T213000Z DTEND:20250109T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/137 DESCRIPTION:Title: Complex structures on nilpotent almost abelian Lie algebras\ nby Romina M. Arroyo (Universidad Nacional de Cordoba) as part of SFU NT-A G seminar\n\nLecture held in K9509.\n\nAbstract\nThe question of which nil potent Lie algebras admit complex structures is far from being understood. In recent decades\, progress has primarily focused on providing algebraic obstructions to the existence of such structures\, with classification re sults being limited to low-dimensional cases.\n\nThe aim of this talk is t o introduce the key concepts necessary to understand the problem\, includi ng the definition of (nilpotent) Lie algebras\, the notion of a complex st ructure on them\, etc. Additionally\, I will present a recent classificati on result for nilpotent almost abelian Lie algebras\, which was obtained t hrough collaborative work with María Laura Barberis\, Verónica Díaz\, Y amile Godoy\, and María Isabel Hernández.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Gordon (UBC) DTSTART:20250306T213000Z DTEND:20250306T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/138 DESCRIPTION:Title: Improving integrability bounds for Harish-Chandra characters \nby Julia Gordon (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9 509.\n\nAbstract\nIt is a well-known result of Harish-Chandra that most in variant distributions on real and p-adic reductive groups (e.g.\, Fourier transforms of orbital integrals\, and characters of representations) are represented by locally integrable functions on the group\, and the singula rities of these functions are `smoothed' by the zeroes of the Weyl discri minant. In the recent joint work with Itay Glazer and Yotam Hendel\, we a nalyze the singularities of the inverse of the Weyl discriminant\, and fro m that\, obtain an explicit improvement on the integrability exponent of t he Fourier transforms of nilpotent orbital integrals\, and consequently\, of characters (all these objects will be defined in the talk). I will disc uss this improvement and some surprising applications\, e.g.\, to word map s.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (SFU) DTSTART:20250130T213000Z DTEND:20250130T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/139 DESCRIPTION:Title: Koszul-Tate Resolutions and Cotangent Cohomology for Monomial Id eals\nby Nathan Ilten (SFU) as part of SFU NT-AG seminar\n\nLecture he ld in K9509.\n\nAbstract\nIntroduced by Tate in 1957\, a Koszul-Tate resol ution allows one to replace any algebra with a free differential graded al gebra. This can be used to compute important invariants of the original al gebra such as BRST cohomology or cotangent cohomology. I will report on a re-interpretation of recent work by Hancharuk\, Laurent-Gengoux\, and Stro bl that constructs explicit Koszul-Tate resolutions. Using this\, I will t hen discuss some work in progress on higher cotangent cohomology for quoti ents of polynomial rings by monomial ideals. This is joint with Francesco Meazzini and Andrea Petracci. No prior knowledge of Koszul-Tate resolution s or cotangent cohomology is assumed.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Jen Berg (Bucknell University) DTSTART:20250327T203000Z DTEND:20250327T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/140 DESCRIPTION:Title: Odd order transcendental obstructions to the Hasse principle on general K3 surfaces\nby Jen Berg (Bucknell University) as part of SFU NT-AG seminar\n\n\nAbstract\nVarieties that fail to have rational points d espite having local points for each prime are said to fail the Hasse princ iple. A systematic tool accounting for these failures uses the Brauer grou p to define an obstruction set known as the Brauer-Manin set. After fixing numerical invariants such as dimension\, it is natural to ask which birat ional classes of varieties fail the Hasse principle\, and moreover whether the Brauer group always explains this failure. In this talk\, we'll focus on K3 surfaces (e.g.\, a double cover of the plane branched along a smoot h sextic curve) which are relatively simple surfaces in terms of geometric complexity\, but have rich arithmetic. Via a purely geometric approach\, we construct a 3-torsion transcendental Brauer class on a degree 2 K3 surf ace which obstructs the Hasse principle\, giving the first example of an o bstruction of this type. This was joint work with Tony Varilly-Alvarado.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Greg Knapp (University of Calgary) DTSTART:20250403T203000Z DTEND:20250403T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/141 DESCRIPTION:Title: Upper bounds on polynomial root separation\nby Greg Knapp (U niversity of Calgary) as part of SFU NT-AG seminar\n\nLecture held in K950 9.\n\nAbstract\nDistances between the roots of a fixed polynomial appear o rganically in many places in number theory. For any $f(x) \\in \\mathbb{Z }[x]$\, let $\\operatorname{sep}(f)$ denote the minimum distance between d istinct roots of $f(x)$. Mahler initiated the study of separation by givi ng lower bounds on $\\operatorname{sep}(f)$ in terms of the degree and Mah ler measure of $f(x)$\, and these bounds have been improved and generalize d in recent years. However\, there has been relatively little study conce rning upper bounds on $\\operatorname{sep}(f)$. In this talk\, I will des cribe recent work with Chi Hoi Yip in which we provide sharp upper bounds on $\\operatorname{sep}(f)$ using techniques from the geometry of numbers. \n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Diana Mocanu (MPIM) DTSTART:20250313T163000Z DTEND:20250313T173000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/142 DESCRIPTION:Title: Generalized Fermat equations over totally real fields\nby Di ana Mocanu (MPIM) as part of SFU NT-AG seminar\n\n\nAbstract\nWiles’ fam ous proof of Fermat’s Last Theorem pioneered the so-called modular metho d\, in which modularity of elliptic curves is used to show that all intege r solutions of Fermat’s equation are trivial.\n\nIn this talk\, we brief ly sketch a variant of the modular method described by Freitas and Siksek in 2014\, proving that for sufficiently large exponents\, Fermat’s Last Theorem holds in five-sixths of real quadratic fields. We then extend this method to explore solutions to two broader Fermat-type families of equati ons. The main ingredients are modularity\, level lowering\, image of inert ia comparisons\, and S-unit equations.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Pries (Colorado State) DTSTART:20250320T203000Z DTEND:20250320T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/143 DESCRIPTION:Title: Supersingular curves in Hurwitz families\nby Rachel Pries (C olorado State) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nA bstract\nDespite extensive research\, it is not known whether Oort's conje cture about the existence of supersingular curves is true or false. In th e first part of the talk\, I will describe supersingular curves and\ndiscu ss the status of Oort's conjecture (both evidence for and counter-indicati ons). In the second part of the talk\, I will explain: new existence resu lts for supersingular curves of low genus (joint work with Booher)\; and m ass formulas for the number of supersingular curves in families (joint wor k with Cavalieri and Mantovan). This latter project generalizes the Eichl er--Deuring mass formula for supersingular elliptic curves. If time permi ts\, I will talk about basic reductions of genus four curves having an aut omorphism of order 5 (joint work with Li\, Mantovan\, Tang).\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/143/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine Leudière (University of Calgary) DTSTART:20250529T203000Z DTEND:20250529T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/144 DESCRIPTION:Title: A computation on Drinfeld modules\nby Antoine Leudière (Uni versity of Calgary) as part of SFU NT-AG seminar\n\nLecture held in K9509. \n\nAbstract\nThe development of algebraic geometry has shed light on deep similarities between the classical number theory (characteristic zero\, n umber fields)\, and its positive characteristic analogue (centered on curv es and function fields). The latter turned out easier to work with: from a theoretical point of view\, some results are unconditional (e.g. Riemann hypothesis for function fields)\; from a computational point of view\, a l ot of elementary procedures can be performed efficiently (e.g. polynomial factorization\, as opposed to integer factorization).\n\nIn this talk\, we will motivate Drinfeld modules: objects that play the role for function f ields that elliptic curves play for number fields. We will give the exampl e of the computation of a group action from Class Field Theory whose class ical analogue is used in isogeny-based cryptography\, and rather slow to c ompute.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/144/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabien Pazuki (University of Copenhagen) DTSTART:20250918T203000Z DTEND:20250918T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/145 DESCRIPTION:Title: Isogeny volcanoes: an ordinary inverse problem.\nby Fabien P azuki (University of Copenhagen) as part of SFU NT-AG seminar\n\nLecture h eld in K9509.\n\nAbstract\nIsogenies between elliptic curves have attracte d a lot of attention\, and over finite fields the structures that they gen erate are fascinating. For supersingular primes\, isogeny graphs are very connected. For ordinary primes\, isogeny graphs have a lot of connected co mponents and each of these components has the shape... of a volcano! An $\ \ell$-volcano graph\, to be precise\, with $\\ell$ a prime. We study the f ollowing inverse problem: if we now start by considering a graph that has an $\\ell$-volcano shape (we give a precise definition\, of course)\, how likely is it that this abstract volcano can be realized as a connected com ponent of an isogeny graph?\n\nWe prove that any abstract $\\ell$-volcano graph can be realized as a connected component of the $\\ell$-isogeny grap h of an ordinary elliptic curve defined over $\\mathbb{F}_p$\, where $\\el l$ and $p$ are two different primes. If time permits\, we will touch upon some new applications and new challenges. This is joint work with Henry Ba mbury and Francesco Campagna.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Tarnu (Simon Fraser University) DTSTART:20251016T203000Z DTEND:20251016T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/146 DESCRIPTION:Title: Limiting behavior of Rudin-Shapiro sequence autocorrelations \nby Daniel Tarnu (Simon Fraser University) as part of SFU NT-AG seminar\n \nLecture held in K9509.\n\nAbstract\nThe Rudin-Shapiro polynomials $p_{m} $ were first studied by Rudin\, Shapiro\, and Golay independently nearly 8 0 years ago and are defined recursively by $p_{0}(x) = q_{0}(x) = 1$ and \ n$$ p_{m}(x) = p_{m-1}(x) + x^{2^{m-1}} q_{m-1}(x)\, $$\n$$ q_{m}(x) = p_{ m-1}(x) - x^{2^{m-1}} q_{m-1}(x). $$\nThis class of polynomials benefits f rom rich structure and is of special interest as a subset of Littlewood po lynomials (i.e.\, polynomials with coefficients in $\\{ -1\, 1 \\}$)\, in part due to their having small $L^{4}$ norm\, which is desirable and almos t always unsatisfied by Littlewood polynomials in general. In application\ , uses are found for the Rudin-Shapiro polynomials in varied contexts such as radio and spectroscopy. \n\nIf we let $p_{m}(x) = \\sum_{j=0}^{2^{m}-1 } a_{j}x^{j}$\, the sequence $(a_{0}\, a_{1}\, \\dots\, a_{2^{m}-1})$ is c alled the $m$-th Rudin-Shapiro sequence. We denote by $C_{m}(k)$ the aperi odic autocorrelation at shift $k$ of the $m$-th Rudin-Shapiro sequence:\n$ $ C_{m}(k) = \\sum_{j=0}^{2^{m}-1} a_{j}a_{j+k}\, $$\nwhere it is understo od that $a_{j} = 0$ for $j \\notin [0\, 2^{m}-1]$. These autocorrelations have been studied extensively. It is often difficult to determine or appro ximate $C_{m}(k)$ for any given $m$ and $k$\, but using the structure of $ p_{m}$\, bounds on partial moments of the $C_{m}(k)$ can be deduced. We gi ve the precise orders of $\\sum_{0 < k \\leq x} (C_{m}(k))^{2} $ and $\\ma x_{0 < k \\leq x} |C_{m}(k)|$\, and asymptotic bounds for $\\sum_{0 < k \\ leq x} |C_{m}(k)|$. Furthermore\, we construct an analogue of $|C_{m}(k)|$ on $[0\,1]$ and show that its maximum value occurs uniquely at $x = \\fra c{2}{3}$\, supporting our conjecture that the maximum value of $|C_{m}(k)| $ occurs uniquely at some $k_{m}^{\\ast}$ with $\\lim_{m \\to \\infty} \\f rac{k_{m}^{\\ast}}{2^{m}} = \\frac{2}{3}$. This is joint work with Stephen Choi.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Shabnam Akhtari (Penn State) DTSTART:20250925T203000Z DTEND:20250925T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/147 DESCRIPTION:Title: A Quantitative Primitive Element Theorem\nby Shabnam Akhtari (Penn State) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAb stract\nLet $K$ be an algebraic number field. The Primitive Element Theore m implies that the number field $K$ can be generated over the field of rat ional numbers by a single element of $K$. We call such an element a genera tor of $K$. A simple and natural question is “What is the smallest gener ator of a given number field?” (and how to find it!) In order to express this question more precisely\, we will introduce some height functions. T hen we will discuss some open problems and some recent progress in this ar ea\, including a joint project with Jeff Vaaler and Martin Widmer.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Josiah Foster (University of Oregon) DTSTART:20251023T203000Z DTEND:20251023T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/148 DESCRIPTION:Title: The Lefschetz standard conjectures for Kummer-type hyper-Kaehler varieties\nby Josiah Foster (University of Oregon) as part of SFU NT- AG seminar\n\nLecture held in K9509.\n\nAbstract\nFor a complex projective variety\, the Lefschetz standard conjectures predict the existence of alg ebraic self-correspondences that are inverse to the hard Lefschetz isomorp hisms. They have broad implications for Hodge theory and the theory of mo tives. We describe recent progress on the Lefschetz standard conjectures for irreducible holomorphic symplectic (compact hyper-Kaehler) manifolds o f generalized Kummer deformation type.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Berget (Western Washington University) DTSTART:20251106T213000Z DTEND:20251106T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/149 DESCRIPTION:Title: Euler characteristics of K-classes for pairs of matroids\nby Andrew Berget (Western Washington University) as part of SFU NT-AG semina r\n\nLecture held in K9509.\n\nAbstract\nIn his 2005 PhD thesis on tropica l linear spaces\, Speyer conjectured an upper bound on the number of inter ior faces in a matroid base polytope subdivision of a hypersimplex. This c onjecture can be reduced to determining the sign of the Euler characterist ic of a certain matroid class in the K-theory of the permutohedral variety . In a recent joint work with Alex Fink\, we prove Speyer's conjecture by showing that the requisite Euler characteristic is non-positive for all ma troids\, and extend this to a statement about pairs of matroids on the sam e ground set. In this talk\, I will provide an overview of our strategy an d zoom in on how we extend geometric results for realizable pairs of matro ids to all pairs.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter McDonald (SFU) DTSTART:20251002T203000Z DTEND:20251002T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/150 DESCRIPTION:Title: The Briançon--Skoda property for singular rings via closure ope rations\nby Peter McDonald (SFU) as part of SFU NT-AG seminar\n\nLectu re held in K9509.\n\nAbstract\nIn 1974\, Briançon and Skoda answered a qu estion of Mather\, showing that for $I=(f_1\,\\dots\,f_n)$ an ideal of the coordinate ring at a smooth point on a complex algebraic variety\, there is a containment $\\overline{I^{n+k-1}}\\subseteq I^k$ for all $k\\geq1$. To the dismay of algebraists\, this was achieved using analytic techniques \, leading Lipman and Sathaye in 1981 to supply an algebraic proof to give a similar bound for ideals in regular rings in all characteristics. Gener ally\, this containment fails for singular rings\, though work of many peo ple have given results for singular rings in various settings. In this tal k\, I'll discuss recent joint work with Neil Epstein\, Rebecca RG\, and Ka rl Schwede where we give a characteristic-free proof of the desired contai nment for a large class of singular rings\, implying many of the previousl y-known Brian\\c{c}on--Skoda type results.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/150/ END:VEVENT BEGIN:VEVENT SUMMARY:Allechar Serrano López (Montana State University) DTSTART:20251009T203000Z DTEND:20251009T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/151 DESCRIPTION:Title: Counting number fields\nby Allechar Serrano López (Montana State University) as part of SFU NT-AG seminar\n\n\nAbstract\nA guiding qu estion in arithmetic statistics is: Given a degree $n$ and a Galois group $G$ in $S_n$\, how does the count of number fields of degree $n$ whose nor mal closure has Galois group $G$ grow as their discriminants tend to infin ity? In this talk\, I will give an overview of the history and development of number field asymptotics\, and we will obtain a count for dihedral qua rtic extensions over a fixed number field.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/151/ END:VEVENT BEGIN:VEVENT SUMMARY:Alicia Lamarche (Yau Mathematical Sciences Center) DTSTART:20251127T213000Z DTEND:20251127T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/152 DESCRIPTION:Title: Wonderful Compactifications for the Algebraic Geometer\nby A licia Lamarche (Yau Mathematical Sciences Center) as part of SFU NT-AG sem inar\n\nLecture held in K9509.\n\nAbstract\nGiven a complex Lie group G of adjoint type\, the wonderful compactification Y(G) (originally described by work of DeConcini-Procesi) is a compactification of G by a divisor with simple normal crossings. These groups are specified by their Dynkin diagr ams and corresponding root systems\, from which one can construct a toric variety X(G). In this talk\, we will discuss ongoing work with Aaron Bertr am that aims to succinctly describe the structure of Y(G) and X(G) in term s of birational geometry.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/152/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Frei (Rice University) DTSTART:20251030T203000Z DTEND:20251030T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/153 DESCRIPTION:Title: Cubic fourfolds with birational Fano varieties of lines\nby Sarah Frei (Rice University) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nCubic fourfolds have been classically studied up to birational equivalence\, with a view toward the rationality problem. The Fano variety of lines F(X) on a cubic fourfold X is a hyperkähler manifol d\, and the rationality of X is conjecturally captured by the geometry of F(X). In joint work with C. Brooke and L. Marquand\, building on our previ ous work with X. Qin\, we study pairs of conjecturally irrational cubic fo urfolds with birational Fano varieties of lines. We provide new examples o f pairs of cubic fourfolds with equivalent Kuznetsov components. Moreover\ , we show that the cubic fourfolds themselves are birational.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Staal (University of the Fraser Valley) DTSTART:20251120T213000Z DTEND:20251120T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/154 DESCRIPTION:Title: Recent Examples of Elementary Components of Hilbert Schemes of P oints\nby Andrew Staal (University of the Fraser Valley) as part of SF U NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nI will present some recent progress in the study of Hilbert schemes $\\operatorname{Hilb}^d(\ \mathbb{A}^n)$ of $d$ points in affine space. Specifically\, I will descri be some recent examples of elementary components of Hilbert schemes of poi nts. One infinite family of these answers a question posed by Iarrobino i n the 80's: does there exist an irreducible component of the (local) punct ual Hilbert scheme $\\operatorname{Hilb}^d(\\mathscr{O}_{\\mathbb{A}^n\,p} )$ of dimension less than $(n-1)(d-1)$? A different family of elementary components arises from the Galois closure operation introduced by Bhargava --Satriano. In both situations\, secondary families of elementary compone nts also arise\, providing further new examples of elementary components o f Hilbert schemes of points.\n\nThis is joint work with Matt Satriano (U W aterloo).\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Joshua Turner (UBC) DTSTART:20251113T213000Z DTEND:20251113T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/155 DESCRIPTION:Title: Haiman ideals\, link homology\, and affine Springer fibers\n by Joshua Turner (UBC) as part of SFU NT-AG seminar\n\nLecture held in K95 09.\n\nAbstract\nWe will discuss a class of ideals in a polynomial ring st udied by Mark Haiman in his work on the Hilbert scheme of points and discu ss how they are related to homology of affine Springer fibers\, Khovanov-R ozansky homology of links\, and to the ORS conjecture. We will also discus s how to compute KR-homology using combinatorial braid recursions develope d by Elias and Hogancamp.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/155/ END:VEVENT BEGIN:VEVENT SUMMARY:Felix Thimm (UBC) DTSTART:20260115T213000Z DTEND:20260115T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/156 DESCRIPTION:Title: Wall-Crossing and the DT/PT3 Descendant Correspondence\nby F elix Thimm (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\ nAbstract\nDonaldson–Thomas and Pandharipande–Thomas invariants are tw o ways of counting curves in Calabi-Yau 3-folds\, related by a change of s tability conditions. Wall-crossing is a technique that allows us to compar e enumerative invariants under such a change in stability condition. It ha s emerged as a powerful tool for computations and in the study of properti es of generating series of various types of enumerative invariants. I will present joint work with N. Kuhn and H. Liu on how to use (virtual) locali zation to wall-cross more general invariants with descendant insertions. I n the process I will explain how Juanolou's trick from classical algebraic geometry comes in as a useful and central ingredient.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/156/ END:VEVENT BEGIN:VEVENT SUMMARY:Seda Albayrak (SFU) DTSTART:20260129T213000Z DTEND:20260129T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/157 DESCRIPTION:Title: Quantitative estimates on the size of an intersection of sparse automatic sets\nby Seda Albayrak (SFU) as part of SFU NT-AG seminar\n\ nLecture held in K9509.\n\nAbstract\nIn this talk\, I will talk about use of automata theory in answering problems in number theory. In 1844\, Catal an conjectured that the set consisting of natural numbers of the form $2^n +1$\, $n \\ge 0$ and the set consisting of powers of $3$ has finite inters ection. In fact\, we can answer such question in more generality\, that is \, instead of $2$ and $3$\, we can show this for $k$ and $\\ell$ that are multiplicatively independent (meaning if $k^a=\\ell^b$\, then $a=b=0$). In automata-theoretic terms\, these sets described above are sparse $2$-auto matic and sparse $3$-automatic sets\, respectively. In fact\, a sparse $k$ -automatic set can be more complicated than having elements that are of th e form $k^n$ or $k^n+1$\, and hence\, we are answering an even more genera l question. Moreover\, we also prove our result in a multidimensional sett ing in line with the existing results in the theory of formal languages an d finite automata. We show that the intersection of a sparse $k$-automatic subset of $\\mathbb{N}^d$ and a sparse $\\ell$-automatic subset of $\\mat hbb{N}^d$ is finite and we give effectively computable upper bounds on the size of the intersection in terms of data from the automata that accept t hese sets. We will also see how all of this is related to a conjecture of Erdös.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Villagra Torcomian (SFU) DTSTART:20260226T213000Z DTEND:20260226T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/158 DESCRIPTION:Title: The role of hyperelliptic curves in the modular method\nby L ucas Villagra Torcomian (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nAfter a brief review of the modular method\, in th is talk we will explain how hyperelliptic curves have emerged as an import ant tool in recent years to approach generalized Fermat equations.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/158/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Bruin (SFU) DTSTART:20260205T213000Z DTEND:20260205T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/159 DESCRIPTION:Title: 2-isogenies on Jacobians of genus 3 curves\nby Nils Bruin (S FU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nWe consider isogenies on Jacobians J of genus 3 curves with a kernel that is a maximal isotropic subgroup of the 2-torsion J[2] and confront a phenome non that is new in genus 3: for genus 1 and 2 the codomain is generally ag ain a Jacobian of a curve and we have\nan explicit construction of that cu rve. In the genus 3 case we only obtain that the codomain is a quadratic t wist of a Jacobian.\n\nWe use a construction by Donagi-Livne\, refined by Lehavi-Ritzenthaler that constructs the curve whose Jacobian is the codoma in up to quadratic twist. We refine the construction further to explicitly determine this quadratic twist and use it to compute many examples. The c onstruction requires the specification of a flag on the isogeny kernel and constructs the codomain in steps\, in terms of various Prym varieties.\n\ nThis is joint work with Damara Gagnier.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu Shen (Michigan State University) DTSTART:20260212T213000Z DTEND:20260212T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/160 DESCRIPTION:Title: Picard group action on the category of twisted sheaves\nby Y u Shen (Michigan State University) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nIn this talk\, I will discuss the category of twisted sheaves on a scheme $X$. Let $\\mathcal{M}$ be a quasi-coherent s heaf on $X$\, and $\\alpha$ in $\\mathrm{Br}(X)$. We show that the functor \n$\n- \\otimes_{\\mathcal{O}_X} \\mathcal{M} : \\operatorname{QCoh}(X\, \ \alpha) \\to \\operatorname{QCoh}(X\, \\alpha)\n$\nis naturally isomorphic to the identity functor if and only if $\\mathcal{M}\\cong \\mathcal{O}_{ X}$. As a corollary\, the action of $\\operatorname{Pic}(X)$ on $D^{b}(X\, \\alpha)$ is faithful for any Noetherian scheme $X$. We also show that ta king Brauer twists of varieties does not yield new Calabi--Yau categories. This is joint work with Ting Gong and Yeqin Liu.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/160/ END:VEVENT BEGIN:VEVENT SUMMARY:Janet Page (North Dakota State University) DTSTART:20260402T203000Z DTEND:20260402T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/161 DESCRIPTION:Title: Smooth Surfaces with Maximally Many Lines\nby Janet Page (No rth Dakota State University) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nHow many lines can lie on a smooth surface of degre e d? This classical question in algebraic geometry has been studied since at least the mid 1800s\, when Clebsch gave an upper bound of d(11d-24) fo r the number of lines on a smooth surface of degree d over the complex num bers. Since then\, Segre and then Bauer and Rams have given sharper upper bounds\, the latter of which also holds over fields of characteristic p > d. However\, over a field of characteristic p < d\, there are smooth pro jective surfaces of degree d which break these upper bounds. In this talk \, I’ll give a new upper bound for the number of lines which can lie on a smooth surface of degree d which holds over any field. In addition\, we ’ll fully classify those surfaces which attain this upper bound and talk about some of their other surprising properties. This talk is based on j oint work with Tim Ryan and Karen Smith.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/161/ END:VEVENT BEGIN:VEVENT SUMMARY:Yixin Chen DTSTART:20260409T203000Z DTEND:20260409T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/162 DESCRIPTION:Title: Transcendental Brauer-Manin Obstruction for Hyperelliptic Surfac es\nby Yixin Chen as part of SFU NT-AG seminar\n\nLecture held in K950 9.\n\nAbstract\nThe Brauer–Manin obstruction provides a powerful framewo rk for explaining failures of the Hasse principle for rational points on a lgebraic varieties. While many known examples arise from the algebraic par t of the Brauer group\, comparatively few explicit constructions exhibit g enuinely transcendental obstructions.\n\nIn this talk\, we will present a concrete example of a transcendental Brauer–Manin obstruction to the exi stence of rational points on a $K3$ surface. We will use a hyperelliptic f ibered surface that is birational to this $K3$ surface to help construct t he Brauer-Manin obstruction.\n\nThis example illustrates how fibration tec hniques can be used to produce and control transcendental elements in the Brauer group.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Wills (University of Virginia) DTSTART:20260319T203000Z DTEND:20260319T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/163 DESCRIPTION:Title: Local-to-global principles for zero-cycles\nby Michael Wills (University of Virginia) as part of SFU NT-AG seminar\n\n\nAbstract\nIn a rithmetic geometry\, local-to-global principles capture the ways in which one approaches difficult "global" questions over number fields by studying their "local" analogues over $p$-adic fields. These principles often fail for questions about the rational points of an algebraic variety. However\ , a conjecture of Colliot-Th$\\text{\\'e}$l$\\text{\\`e}$ne states that by generalizing the question to zero-cycles one might recover a successful l ocal-to-global principle. In this talk\, we present some recent evidence f or this conjecture for products of elliptic curves with complex multiplica tion.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/163/ END:VEVENT BEGIN:VEVENT SUMMARY:Graham McDonald (SFU) DTSTART:20260305T213000Z DTEND:20260305T223000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/164 DESCRIPTION:Title: Curves in linear systems on abelian surfaces\nby Graham McDo nald (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstr act\nLet $A$ be an abelian surface. We investigate curves in a linear syst em on the dual abelian surface $\\hat{A}$. There is an isomorphism of modu li spaces due to Yoshioka between the space $K_3(A)$ parametrizing 0-dimen sional length-4 subschemes on $A$ that sum to the identity in the group la w\, and the space $K_{\\hat{A}}(0\,\\hat{\\ell}\,-1)$ parametrizing certai n rank 1 torsion free sheaves supported on curves in a linear system on $\ \hat{A}$. Leveraging this isomorphism together with quadratic forms associ ated to symmetric line bundles on $A$\, we develop a computational method that allows us to characterize the singularities of the curves that corres pond to a finite distinguished subset of $K_3(A)$. In this talk we will de scribe these methods and compute an example of a curve with two nodal sing ularities.\n\nThis is joint work with Katrina Honigs and Peter McDonald.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/164/ END:VEVENT BEGIN:VEVENT SUMMARY:Negarin Mohammadi (Simon Fraser University) DTSTART:20260312T203000Z DTEND:20260312T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/165 DESCRIPTION:Title: Arithmetic Prym Constructions and (1\,2)-Polarized Abelian Surfa ces\nby Negarin Mohammadi (Simon Fraser University) as part of SFU NT- AG seminar\n\nLecture held in K9509.\n\nAbstract\nWe construct explicit ex amples of abelian surfaces whose 2-torsion Galois representations are not self-dual. Such surfaces are necessarily not principally polarized. We con sider abelian surfaces with a polarization of type (1\,2) instead. Our mai n tool is to describe (1\,2)-polarized surfaces as a Prym variety $P$ of a double cover of an elliptic curve by a bielliptic curve $C$ of genus 3. W e use a Galois-theoretic construction of Donagi and Pantazis to express th e dual also as a Prym variety of the same type. The 2-torsion $P[2]$ natur ally embeds in $J_C[2]$\, where the classical geometry of plane quartics\, bitangents\, and theta characteristics gives concrete access to the Galoi s action. \n\nConversely\, we prove that every (1\,2)-polarized abelian su rface over a base field of characteristic other than 2 can be realized as a bielliptic Prym. Barth already proved this over algebraically closed bas e fields\, and we extend it to arbitrary fields. This is achieved by facto ring the polarization $\\rho : A \\to A^\\vee$ through a principally polar ized surface $J$. We then show that an appropriate plane section of the Ku mmer surface of $J$ yields an elliptic curve $E$ with a genus 3 double cov er $C \\to E$ such that $A^\\vee = \\mathrm{Prym}(C \\to E)$. A careful G alois descent argument then allows us to deduce the general case.\n\nThis is joint work with Nils Bruin and Katrina Honigs.\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/165/ END:VEVENT BEGIN:VEVENT SUMMARY:No seminar (PIMS Colloquium) DTSTART:20260326T203000Z DTEND:20260326T213000Z DTSTAMP:20260404T095902Z UID:SFUQNTAG/166 DESCRIPTION:by No seminar (PIMS Colloquium) as part of SFU NT-AG seminar\n \nLecture held in K9509.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SFUQNTAG/166/ END:VEVENT END:VCALENDAR