Joint work with Markus Kirschmer\, Fabien Narbonne and Damien Robert< /p>\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabien Pazuki (Copenhagen) DTSTART:20200521T170000Z DTEND:20200521T180000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/3 DESCRIPTION:Title: Regulators of number fields and abelian varieties\nby Fabien Pazuki ( Copenhagen) as part of SFU NT-AG seminar\n\n\nAbstract\nIn the general stu dy of regulators\, we present three inequalities. We first bound from belo w the regulators of number fields\, following previous works of Silverman and Friedman. We then bound from below the regulators of Mordell-Weil grou ps of abelian varieties defined over a number field\, assuming a conjectur e of Lang and Silverman. Finally we explain how to prove an unconditional statement for elliptic curves of rank at least 4. This third inequality is joint work with Pascal Autissier and Marc Hindry. We give some corollarie s about the Northcott property and about a counting problem for rational p oints on elliptic curves.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (SFU) DTSTART:20200528T223000Z DTEND:20200528T233000Z DTSTAMP:20260422T022949Z 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 Sa lmon showed in 1849 that a smooth cubic surface contains 27 lines\, and Sc hubert showed in 1879 that a generic quintic threefold contains 2875 lines . More generally\, the set of k-dimensional linear spaces contained in a f ixed projective variety X itself is called the k-th Fano scheme of X. Thes e Fano schemes have been studied extensively when X is a general hypersurf ace or complete intersection in projective space.\n\n
In this talk\, I w ill report on work with Tyler Kelly in which we study Fano schemes for hyp ersurfaces and complete intersections in projective toric varieties. In pa rticular\, I'll give criteria for the Fano schemes of generic complete int ersections in a projective toric\nvariety to be non-empty and of "expected dimension". Combined with some intersection theory\, this can be used for enumerative problems\, for example\, to show that a general degree (3\,3) -hypersurface in the Segre embedding of $\\mathbb{P}^2\\times \\mathbb{P}^ 2$ contains exactly 378 lines.
\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Türkü Özlüm Çelik (Leipzig University) DTSTART:20200604T223000Z DTEND:20200604T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/5 DESCRIPTION:Title: The Dubrovin threefold of an algebraic curve\nby Türkü Özlüm Çel ik (Leipzig University) as part of SFU NT-AG seminar\n\n\nAbstract\nThe so lutions to the Kadomtsev-Petviashvili equation that arise from a fixed\nco mplex algebraic curve are parametrized by a threefold in a weighted projec tive space\,\nwhich we name after Boris Dubrovin. Current methods from non linear algebra are applied\nto study parametrizations and defining ideals of Dubrovin threefolds. We highlight the\ndichotomy between transcendental representations and exact algebraic computations.\nThis is joint work with Daniele Agostini and Bernd Sturmfels.
\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jake Levinson (University of Washington) DTSTART:20200611T223000Z DTEND:20200611T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/6 DESCRIPTION:Title: Boij-Söderberg Theory for Grassmannians\nby Jake Levinson (Universit y of Washington) as part of SFU NT-AG seminar\n\n\nAbstract\nThe Betti tab le of a graded module over a polynomial ring encodes much of its structure and that of the corresponding sheaf on projective space. In general\, it is hard to tell which integer matrices can arise as Betti tables. An easie r problem is to describe such tables up to positive scalar multiple: this is the "cone of Betti tables". The Boij-Söderberg conjectures\, proven by Eisenbud-Schreyer\, gave a beautiful description of this cone and\, as a bonus\, a "dual" description of the cone of cohomology tables of sheaves.\ n\nI will describe some extensions of this theory\, joint with Nicolas Ford and Steven Sam\, to the setting of GL-equivariant modules over coordi nate rings of matrices. Here\, the dual theory (in geometry) concerns shea f cohomology on Grassmannians. One theorem of interest is an equivariant a nalog of the Boij-Söderberg pairing between Betti tables and cohomology t ables. This is a bilinear pairing of cones\, with output in the cone comin g from the "base case" of square matrices\, which we also fully characteri ze.
\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Avinash Kulkarni (Darmouth) DTSTART:20200625T223000Z DTEND:20200625T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/7 DESCRIPTION:Title: pNumerical Linear Algebra\nby Avinash Kulkarni (Darmouth) as part of SFU NT-AG seminar\n\n\nAbstract\nIn this talk\, I will present new algorit hms\, based on ideas from numerical analysis\, for efficiently computing t he 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 polynomial syst em.\n\n(Some content ongoing work with T. Vaccon)\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Turchetti (Dalhousie) DTSTART:20200702T223000Z DTEND:20200702T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/8 DESCRIPTION:Title: Moduli spaces of Mumford curves over Z\nby Daniele Turchetti (Dalhous ie) as part of SFU NT-AG seminar\n\n\nAbstract\nSchottky uniformization is the description of an analytic curve as the quotient of an open dense sub set of the projective line by the action of a Schottky group.\nAll complex curves admit this uniformization\, as well as some $p$-adic curves\, call ed Mumford curves.\nIn this talk\, I present a construction of universa l Mumford curves\, analytic spaces that parametrize both archimedean a nd non-archimedean uniformizable curves of a fixed genus.\nThis result rel ies on the existence of suitable moduli spaces for marked Schottky groups\ , that can be built using the theory of Berkovich spaces over rings of int egers of number fields due to Poineau.\nAfter introducing Poineau's the ory from scratch\, I will describe universal Mumford curves and explain ho w these can be used as a framework to study the Tate curve and to give hig her genus generalizations of it. This is based on joint work with Jérôme Poineau.
\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Várilly-Alvarado (Rice University) DTSTART:20200709T223000Z DTEND:20200709T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/9 DESCRIPTION:Title: Rational surfaces and locally recoverable codes\nby Anthony Várilly- Alvarado (Rice University) as part of SFU NT-AG seminar\n\n\nAbstract\nMot ivated by large-scale storage problems around data loss\, a budding branch of coding theory has surfaced in the last decade or so\, centered around locally recoverable codes. These codes have the property that individual s ymbols in a codeword are functions of other symbols in the same word. If a symbol is lost (as opposed to corrupted)\, it can be recomputed\, and hen ce a code word can be repaired. Algebraic geometry has a role to play in t he design of codes with locality properties. In this talk I will explain h ow to use algebraic surfaces birational to the projective plane to both re interpret constructions of optimal codes already found in the literature\, and to find new locally recoverable codes\, many of which are optimal (in a suitable sense). This is joint work with Cecília Salgado and Felipe Vo loch.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Bianca Viray (University of Washington) DTSTART:20200716T223000Z DTEND:20200716T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/10 DESCRIPTION:Title: Isolated points on modular curves\nby Bianca Viray (University of Wa shington) as part of SFU NT-AG seminar\n\n\nAbstract\nFaltings's theorem o n rational points on subvarieties of\nabelian varieties can be used to sho w that all but finitely many\nalgebraic points on a curve arise in familie s parametrized by $\\mathbb{P}^1$ or\npositive rank abelian varieties\; we call these finitely many\nexceptions isolated points. We study how isola ted points behave under\nmorphisms and then specialize to the case of modu lar curves. We show\nthat isolated points on $X_1(n)$ push down to isolat ed points on a\nmodular curve whose level is bounded by a constant that de pends only\non the j-invariant of the isolated point. This is joint work with A.\nBourdon\, O. Ejder\, Y. Liu\, and F. Odumodu.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Brendan Creutz (University of Canterbury) DTSTART:20200723T223000Z DTEND:20200723T233000Z DTSTAMP:20260422T022949Z 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 NT-AG se minar\n\n\nAbstract\nFor a curve C over a global field K it has been conje ctured that the Brauer-Manin obstruction explains all failures of the Hass e principle. I will discuss results toward this conjecture in the case of constant curves over a global function field\, i.e. where C and D are curv es over a finite field and we consider C over the function field of D. Thi s is joint work with Felipe Voloch.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosa Winter (MPI MiS) DTSTART:20201029T163000Z DTEND:20201029T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/12 DESCRIPTION:Title: Density of rational points on a family of del Pezzo surfaces of degree $ 1$\nby Rosa Winter (MPI MiS) as part of SFU NT-AG seminar\n\n\nAbstrac t\nDel Pezzo surfaces are classified by their degree d\, which is an integ er between $1$ and $9$ (for $d ≥ 3$\, these are the smooth surfaces of d egree $d$ 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 is Zaris ki dense provided that the surface has one $k$-rational point to start wit h (that lies outside a specific subset of the surface for degree $2$). How ever\, for del Pezzo surfaces of degree $1$ over a field k\, even though w e know that they always contain at least one $k$-rational point\, we do no t know if the set of $k$-rational points is Zariski dense in general. I wi ll talk about a result that is joint work with Julie Desjardins\, in which we give necessary and sufficient conditions for the set of $k$-rational p oints on a specific family of del Pezzo surfaces of degree $1$ to be Zaris ki dense\, where k is a number field. I will compare this to previous resu lts.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Enis Kaya (University of Groningen) DTSTART:20201105T173000Z DTEND:20201105T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/13 DESCRIPTION:Title: Explicit Vologodsky Integration for Hyperelliptic Curves\nby Enis Ka ya (University of Groningen) as part of SFU NT-AG seminar\n\n\nAbstract\nL et $X$ 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 notions of p- adic integration one may associate \nto this data: the Berkovich–Coleman integral which can be performed locally\; and the \nVologodsky integral w ith desirable number-theoretic properties. In this talk\, we present a \nt heorem comparing the two\, and describe an algorithm for computing Vologod sky integrals \nin the case that $X$ is a hyperelliptic curve. We also ill ustrate our algorithm with a numerical \nexample computed in Sage. This ta lk is partly based on joint work with Eric Katz.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Elisa Lorenzo García (Universtiy of Rennes 1) DTSTART:20201112T173000Z DTEND:20201112T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/14 DESCRIPTION:Title: Primes of bad reduction for CM curves of genus 3 and their exponents on the discriminant\nby Elisa Lorenzo García (Universtiy of Rennes 1) as part of SFU NT-AG seminar\n\n\nAbstract\nLet O be an order in a sextic 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 to contr ol the primes in the discriminant of the curves and their exponents. In pr evious works I studied the so-called "embedding problem" in order to bound the primes of bad reduction. In the present one we give an algorithm to e xplicitly compute them and we bound the exponent of those primes in the di scriminant for the hyperelliptic case. Several examples will be given.\n\n (joint work with S. Ionica\, P. Kilicer\, K. Lauter\, A. Manzateanu and C. Vincent)\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Sertöz (Max Planck Institute for Mathematics) DTSTART:20201126T173000Z DTEND:20201126T183000Z DTSTAMP:20260422T022949Z 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\nAbstract\nKon tsevich--Zagier periods form a natural number system that extends the alge braic numbers by adding constants coming from geometry and physics. Becaus e there are countably many periods\, one would expect it to be possible to compute effectively in this number system. This would require an effectiv e height function and the ability to separate periods of bounded height\, neither of which are currently possible.\n\nIn this talk\, we introduce an effective height function for periods of quartic surfaces defined over al gebraic numbers. We also determine the minimal distance between periods of bounded height on a single surface. We use these results to prove heurist ic computations of Picard groups that rely on approximations of periods. M oreover\, we give explicit Liouville type numbers that can not be the rati o of two periods of a quartic surface. This is ongoing work with Pierre La irez (Inria\, France).\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Monagan (Simon Fraser University) DTSTART:20201119T173000Z DTEND:20201119T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/16 DESCRIPTION:Title: The Tangent-Graeffe root finding algorithm\nby Michael Monagan (Simo n Fraser University) as part of SFU NT-AG seminar\n\n\nAbstract\nLet $f(x) $ be a polynomial of degree $d$ over a prime field of size $p$.\nSuppose $ f(x)$ has $d$ distinct roots in the field and we want to compute them.\nQu estion: How fast can we compute the roots?\n\nThe most well known method i s the Cantor-Zassenhaus algorithm from 1981.\nIt is implemented in Maple a nd Magma. It does\, on average\, $O(M(d) \\log d \\log p)$\narithmetic op erations in the field where $M(d)$ is the cost of multiplying two \npolyno mials of degree $\\le d$.\n\nIn 2015 Grenet\, van der Hoeven and Lecerf fo und 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 the new\n method by a constant factor and a C implementation of the new method\nusin g asymptotically fast polynomial arithmetic.\n\nIn the talk I will present the main ideas behind the new Tangent-Graeffe algorithm\,\nsome timings c omparing the Tangent Graeffe algorithm with the Cantor-Zassenhaus \nalgori thm in Magma\, and a new polynomial factorization world record.\n\nThis is joint work with Joris van der Hoeven.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Marseglia (Utrecht University) DTSTART:20201203T173000Z DTEND:20201203T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/17 DESCRIPTION:Title: Products and Polarizations of Super-Isolated Abelian Varieties\nby S tefano Marseglia (Utrecht University) as part of SFU NT-AG seminar\n\n\nAb stract\nSuper-isolated abelian varieties are abelian varieties over finite fields whose isogeny class contains a single isomorphism class. In this t alk we will review their properties\, consider their products and\, in the ordinary case\, we will describe their (principal) polarizations.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Agostini (MPI MiS) DTSTART:20201210T173000Z DTEND:20201210T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/18 DESCRIPTION:Title: On the irrationality of moduli spaces of K3 surfaces\nby Daniele Ago stini (MPI MiS) as part of SFU NT-AG seminar\n\n\nAbstract\nIn this talk\, we consider quantitative measures of irrationality for moduli\nspaces of polarized K3 surfaces of genus g. We show that\, for infinitely many examp les\,\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 c ertain modular form of weight 11. This is joint work with Ignacio Barros a nd Kuan-Wen Lai.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeline Brandt (Brown University) DTSTART:20210121T173000Z DTEND:20210121T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/19 DESCRIPTION:Title: Top Weight Cohomology of $A_g$\nby Madeline Brandt (Brown University ) as part of SFU NT-AG seminar\n\n\nAbstract\nI will discuss a recent proj ect in computing the top weight cohomology of the moduli space $A_g$ of pr incipally polarized abelian varieties of dimension $g$ for small values of $g$. This piece of the cohomology is controlled by the combinatorics of t he boundary strata of a compactification of $A_g$. Thus\, it can be comput ed combinatorially. This is joint work with Juliette Bruce\, Melody Chan\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Anwesh Ray (University of British Columbia) DTSTART:20210128T173000Z DTEND:20210128T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/20 DESCRIPTION:Title: Level Lowering via the Deformation theory of Galois Representations\ nby Anwesh Ray (University of British Columbia) as part of SFU NT-AG semin ar\n\n\nAbstract\nElliptic curves defined over the rational numbers arise from \ncertain modular forms. This is the celebrated Modularity theorem of Wiles \net al. Prior to this development\, Ribet had proved a level lower ing \ntheorem\, thanks to which one is able to optimize the level of the m odular \nform in question. Ribet's theorem combined with the modularity th eorem of \nWiles together imply Fermat's Last theorem.\n\nIn joint work wi th Ravi Ramakrishna\, we develop some new techniques to\nprove level lower ing results for more general Galois representations.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Heaton (The Fields Institute) DTSTART:20210225T173000Z DTEND:20210225T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/21 DESCRIPTION:Title: Catastrophe discriminants of tensegrity frameworks\nby Alex Heaton ( The Fields Institute) as part of SFU NT-AG seminar\n\n\nAbstract\nWe discu ss elastic tensegrity frameworks made from rigid bars and elastic cables\, depending on many parameters. For any fixed parameter values\, the stable equilibrium position of the framework is determined by minimizing an ener gy function subject to algebraic constraints. As parameters smoothly chang e\, it can happen that a stable equilibrium disappears. This loss of equil ibrium is called `catastrophe' since the framework will experience large-s cale shape changes despite small changes of parameters. Using nonlinear al gebra we characterize a semialgebraic subset of the parameter space\, the catastrophe set\, which detects the merging of local extrema from this par ametrized family of constrained optimization problems\, and hence detects possible catastrophe. Tools from numerical nonlinear algebra allow reliabl e and efficient computation of all stable equilibrium positions as well as the catastrophe set itself.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Fanelli DTSTART:20210204T173000Z DTEND:20210204T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/22 DESCRIPTION:Title: Del Pezzo fibrations in positive characteristic\nby Andrea Fanelli a s part of SFU NT-AG seminar\n\n\nAbstract\nIn this talk\, I will discuss s ome pathologies for the generic fibre of del Pezzo fibrations in character istic $p>0$\, \nmotivated by the recent developments of the MMP in positiv e characteristic. The recent joint work with \nStefan Schröer applies to deduce information on the structure of 3-dimensional Mori fibre spaces and \nanswers an old question by János Kollár.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Elina Robeva (University of British Columbia) DTSTART:20210415T163000Z DTEND:20210415T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/23 DESCRIPTION:Title: Hidden Variables in Linear Causal Models\nby Elina Robeva (Universit y of British Columbia) as part of SFU NT-AG seminar\n\n\nAbstract\nIdentif ying causal relationships between random variables from observational data is an important hard problem in many areas of data science. The presence of hidden variables\, though quite realistic\, pauses a variety of further problems. Linear structural equation models\, which express each variable as a linear combination of all of its parent variables\, have long been u sed for learning causal structure from observational data. Surprisingly\, when the variables in a linear structural equation model are non-Gaussian the full causal structure can be learned without interventions\, while in the Gaussian case one can only learn the underlying graph up to a Markov e quivalence class. In this talk\, we first discuss how one can use high-ord er cumulant information to learn the structure of a linear non-Gaussian st ructural equation model with hidden variables. While prior work posits tha t each hidden variable is the common cause of two observed variables\, we allow each hidden variable to be the common cause of multiple observed var iables. Next\, we discuss hidden variable Gaussian causal models and the d ifficulties that arise with learning those. We show it is hard to even des cribe the Markov equivalence classes in this case\, and we give a semi alg ebraic description of a large class of these models.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Lian Duan (Colorado State University) DTSTART:20210408T163000Z DTEND:20210408T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/24 DESCRIPTION:Title: Bertini's theorem over finite field and Frobenius nonclassical varieties \nby Lian Duan (Colorado State University) as part of SFU NT-AG semina r\n\n\nAbstract\nLet X be a smooth subvariety of $\\mathbb{P}^n$ defined o ver a field k. Suppose k is an infinite field\, then the classical theorem of Bertini asserts that X admits a smooth hyperplane section. However\, i f k is a finite field\, there are examples of X such that every hyperplane H in $\\mathbb{P}^n$ defined over k is tangent to X. One of the remedies in this situation is to extending the ground field k to its finite extensi on\, 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)\, ho w much one needs to extend k in order to guarantee at least one transvers e hyperplane section? In this talk we will report several results regardin g to this type of questions. We also want to talk about a special type 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://researchseminars.org/talk/SFUQNTAG/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Alp Bassa (Boğaziçi University) DTSTART:20210304T173000Z DTEND:20210304T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/25 DESCRIPTION:Title: Rational points on curves over finite fields and their asymptotic\nb y Alp Bassa (Boğaziçi University) as part of SFU NT-AG seminar\n\n\nAbst ract\nCurves over finite fields with many rational points have been of int erest for both theoretical reasons and for applications. To obtain such cu rves with large genus various methods have been employed in the past. One such method is by means of explicit recursive equations and will be the em phasis of this talk. The recursive nature of these towers makes them very special and in fact all good examples have been shown to have a modular in terpretation of some sort. In this talk I will try to give an overview of the landscape of explicit recursive towers and their modularity.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Asher Auel (Dartmouth College) DTSTART:20210318T163000Z DTEND:20210318T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/26 DESCRIPTION:Title: The local-global principle for quadratic forms over function fields\ nby Asher Auel (Dartmouth College) as part of SFU NT-AG seminar\n\n\nAbstr act\nThe Hasse-Minkowski theorem says that a quadratic form over a global field admits a nontrivial zero if it admits a nontrivial zero everywhere l ocally. Over more general fields of arithmetic and geometric interest\, th e failure of the local-global principle is often controlled by auxiliary s tructures of interest\, such as torsion points of the Jacobian and the Bra uer group. I will explain work with V. Suresh on the failure of the local -global principle for quadratic forms over function fields varieties of di mension at least two. The counterexamples we construct are controlled by higher unramified cohomology groups and involve the study of Calabi-Yau va rieties of generalized Kummer type that originally arose from number theor y. Along the way\, we need to develop an arithmetic version of a result o f Gabber on the nontriviality of certain unramified cohomology classes on products of elliptic curves.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Ari Shnidman (Hebrew University of Jerusalem) DTSTART:20210325T163000Z DTEND:20210325T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/27 DESCRIPTION:Title: Selmer groups of abelian varieties with cyclotomic multiplication\nb y Ari Shnidman (Hebrew University of Jerusalem) as part of SFU NT-AG semin ar\n\n\nAbstract\nLet $A$ be an abelian variety over a number field $F$\, with complex multiplication by the $n$-th cyclotomic field $\\mathbb{Q}(\\ zeta)$. 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. Mor e generally\, we prove average rank bounds for various twist families of a belian varieties with "cyclotomic" multiplication (not necessarily CM) ove r $\\bar F$\, such as sextic twist families of trigonal Jacobians over $\\ mathbb{Q}$. These results have application to questions of "rank gain" f or 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 fixed cu rve $C$ of genus $ g > 1$. This is joint work with Ariel Weiss.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Fevola (MPI MiS) DTSTART:20210311T173000Z DTEND:20210311T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/28 DESCRIPTION:Title: KP Solitons from Tropical Limits\nby Claudia Fevola (MPI MiS) as par t of SFU NT-AG seminar\n\n\nAbstract\nIn this talk\, we present solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves u ndergo tropical degenerations. Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We introduce th e Hirota variety which parametrizes all tau functions arising from such a sum. After introducing solitons solutions\, we compute tau functions from points on the Sato Grassmannian that represent Riemann-Roch spaces.\nThis is joint work with Daniele Agostini\, Yelena Mandelshtam and Bernd Sturmfe ls.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Tristan Vaccon (Université de Limoges) DTSTART:20210401T163000Z DTEND:20210401T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/29 DESCRIPTION:Title: On Gröbner bases over Tate algebras\nby Tristan Vaccon (Université de Limoges) as part of SFU NT-AG seminar\n\n\nAbstract\nTate series are a generalization of polynomials introduced by John Tate in 1962\, when defi ning a p-adic analogue of the correspondence between algebraic geometry an d analytic geometry. This p-adic analogue is called rigid geometry\, and T ate series\, similar to analytic functions in the complex case\, are its f undamental objects. Tate series are defined as multivariate formal power s eries over a p-adic ring or field\, with a convergence condition on a clos ed ball.\n\nTate series are naturally approximated by multivariate polynom ials over F_p or Z/p^n Z\, and it is possible to define a theory of Gröbn er bases for ideals of Tate series\, which opens the way towards effective rigid geometry. \n\nIn this talk\, I will present classical algorithms to compute Gröbner bases (Buchberger\, F5\, FGLM) and how they can be adap ted for Tate series.\n\nJoint work with Xavier Caruso and Thibaut Verron.\ n LOCATION:https://researchseminars.org/talk/SFUQNTAG/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Özlem Ejder (Boğaziçi University) DTSTART:20210527T163000Z DTEND:20210527T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/30 DESCRIPTION:Title: Galois theory of Dynamical Belyi Maps\nby Özlem Ejder (Boğaziçi U niversity) as part of SFU NT-AG seminar\n\n\nAbstract\nLet $f: \\mathbb{P} ^1_K \\rightarrow \\mathbb{P}^1_K$ 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 thi s talk\, we will discuss the various Galois groups attached to the iterate s of $f$\, namely arithmetic and geometric monodromy groups and Arboreal G alois representations. While providing a survey of recent results on the s ubject\, we will also talk about joint work with I. Bouw and V. Karemaker on Dynamical Belyi maps.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Lara Bossinger (Instituto de Matemáticas UNAM) DTSTART:20210610T163000Z DTEND:20210610T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/31 DESCRIPTION:Title: Projections in toric degenerations and standard monomials\nby Lara B ossinger (Instituto de Matemáticas UNAM) as part of SFU NT-AG seminar\n\n \nAbstract\nI will report on joint work in progress with Takuya Murata. We study toric degenerations\, i.e. flat morphism of a normal variety to the affine line whose generic fibre is isomorphic to a fixed projective varie ty and whose special fibre is a projective toric variety. Although such a flat morphism may be given abstractly (i.e. without an embedding\, for exa mple a toric scheme over the affine line) using valuations and Gröbner th eory we may restrict our attention to the case where our family comes endo wed with an embedding. I will illustrate an example of an elliptic curve w here a toric degeneration admits a projection from the generic fibre (the elliptic curve) to the special fibre (the toric curve). We want to underst and which kind of (embedded) toric degenerations admit such a projection. The notion of standard monomials in Gröbner theory proves to be a useful tool in constructing projections in arbitrary toric degenerations.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Soumya Sankar (Ohio State University) DTSTART:20210708T163000Z DTEND:20210708T173000Z DTSTAMP:20260422T022949Z 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 c lassical problem of counting elliptic curves with a rational N-isogeny can be phrased in terms of counting rational points on certain moduli stacks of elliptic curves. Counting points on stacks poses various challenges\, a nd I will discuss these along with a few ways to overcome them. I will als o talk about the theory of heights on stacks developed in recent work of E llenberg\, Satriano and Zureick-Brown and use it to count elliptic curves with an N-isogeny for certain N. The talk assumes no prior knowledge of st acks and is based on joint work with Brandon Boggess.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Mateusz Michałek (University of Konstanz) DTSTART:20210624T163000Z DTEND:20210624T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/33 DESCRIPTION:Title: Chromatic polynomials of tensors and cohomology of complete forms\nb y Mateusz Michałek (University of Konstanz) as part of SFU NT-AG seminar\ n\n\nAbstract\nThere are two plane quadrics passing through four general p oints and tangent to one general line. There are six ways to properly colo r vertices of a triangle with three colors. The maximum likelihood functio n for a general linear concentration two dimensional model in a four dimen sional space has three critical points. Each of these examples of course c omes naturally in families.\nIn our talk we will try to explain what the a bove numbers mean\, how to compute them and that they are all shadows of t he same construction. Our methods are based on the cohomology ring of the so-called variety of complete forms.\nThe talk is based on works with Conn er\, Dinu\, Manivel\, Monin\, Seynnaeve\, Wisniewski and Vodicka. These ar e on the other hand based on fundamental works due to Huh\, Pragacz\, Stur mfels\, Teissier\, Uhler and others (Schubert included).\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Melissa Sherman-Bennett (UC Berkeley) DTSTART:20210715T163000Z DTEND:20210715T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/34 DESCRIPTION:Title: The hypersimplex and the m=2 amplituhedron: Eulerian numbers\, sign flip s\, triangulations\nby Melissa Sherman-Bennett (UC Berkeley) as part o f SFU NT-AG seminar\n\n\nAbstract\nPhysicists Arkhani-Hamed and Trnka intr oduced the amplituhedron to better understand scattering amplitudes in N=4 super Yang-Mills theory. The amplituhedron is the image of the totally no nnegative Grassmannian under the "amplituhedron map"\, which is induced by matrix multiplication. Examples of amplituhedra include cyclic polytopes\ , the totally nonnegative Grassmannian itself\, and cyclic hyperplane arra ngements. In general\, the amplituhedron is not a polytope. However\, Luko wski--Parisi--Williams noticed a mysterious connection between the m=2 amp lituhedron 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 this corre spondence. Along the way\, we prove an intrinsic description of the m=2 am plituhedron conjectured by Arkhani-Hamed--Thomas--Trnka\; give a decomposi tion of the m=2 amplituhedron into Eulerian number-many sign chambers\, in direct analogy to a triangulation of the hypersimplex\; and find new clus ter varieties in the Grassmannian.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Selvi Kara (University of South Alabama) DTSTART:20210617T163000Z DTEND:20210617T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/35 DESCRIPTION:Title: Blow-Up Algebras of Strongly Stable Ideals\nby Selvi Kara (Universit y 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 ideals in $ S$. The multi-Rees algebra $\\mathcal{R} (I_1\,\\ldots\, I_r)$ of this col lection of ideals encode many algebraic properties of these ideals\, their products\, and powers. Additionally\, the multi-Rees algebra $\\mathcal{ R} (I_1\,\\ldots\, I_r)$ arise in successive blowing up of $\\textrm{Spec } S$ at the subschemes defined by $I_1\,\\ldots\, I_r$. Due to this connec tion\, Rees and multi-Rees algebras are also called blow-up algebras in th e literature.\n\nIn this talk\, we will focus on Rees and multi-Rees algeb ras of strongly stable ideals. In particular\, we will discuss the Koszuln ess of these algebras through a systematic study of these objects via thre e parameters: the number of ideals in the collection\, the number of Borel generators of each ideal\, and the degrees of Borel generators. In our st udy\, we utilize combinatorial objects such as fiber graphs to detect Grö bner bases and Koszulness of these algebras. This talk is based on a joint work with Kuei-Nuan Lin and Gabriel Sosa.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Yairon Cid-Ruiz (Ghent University) DTSTART:20210722T163000Z DTEND:20210722T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/36 DESCRIPTION:Title: Primary decomposition with differential operators.\nby Yairon Cid-Ru iz (Ghent University) as part of SFU NT-AG seminar\n\n\nAbstract\nWe intro duce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the arithmetic multiplicity. Minimal diffe rential primary decompositions are unique up to change of bases. Our resul ts generalize the construction of Noetherian operators for primary ideals in the analytic theory of Ehrenpreis-Palamodov\, and they offer a concise method for representing affine schemes. The case of modules is also addres sed. This is joint work with Bernd Sturmfels.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Anwesh Ray (University of British Columbia) DTSTART:20210729T163000Z DTEND:20210729T173000Z DTSTAMP:20260422T022949Z 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 seminar\n \n\nAbstract\nAn elliptic curve defined over the rationals gives rise to a \ncompatible system of Galois representations. The Iwasawa invariants \na ssociated to these representations epitomize their arithmetic and Iwasawa \ntheoretic properties. The study of these invariants is the subject of mu ch \nconjecture and contemplation. For instance\, according to a long-stan ding \nconjecture of R. Greenberg\, the Iwasawa "mu-invariant" must vanish \, subject \nto mild hypothesis. Overall\, there is a subtle relationship between the \nbehavior of these invariants and the p-adic Birch and Swinne rton-Dyer \nformula. We study the behaviour of these invariants on average \, where \nelliptic curves over the rationals are ordered according to hei ght. I will \ndiscuss some recent results (joint with Debanjana Kundu) in which we set \nout new directions in arithmetic statistics and Iwasawa the ory.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Gillespie (Colorado State University) DTSTART:20210812T163000Z DTEND:20210812T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/38 DESCRIPTION:Title: Lazy tournaments\, slide rules\, and multidegrees of projective embeddin gs of M_{0\,n}-bar\nby Maria Gillespie (Colorado State University) as part of SFU NT-AG seminar\n\n\nAbstract\nWe present a combinatorial algori thm on trivalent trees that we call a lazy tournament\, which gives rise t o a new geometric interpretation of the multidegrees of a projective embed ding of the moduli space M_{0\,n}-bar of stable n-marked genus 0 curves. We will show that the multidegrees are enumerated by disjoint sets of boun dary points of the moduli space that can be seen to total (2n-7)!!\, givin g a natural proof of the value of the total degree. These sets are compat ible with the forgetting maps used to derive the previously known recursio n for the multidegrees.\n\nAs time permits\, we will discuss an alternativ e combinatorial construction of (non-disjoint) sets of boundary points tha t enumerate the multidegrees\, via slide rules\, that can in fact be achie ved geometrically via a degeneration of intersections with hyperplanes in the projective embedding. These combinatorial rules further generalize to give a positive expansion of any product of psi or omega classes on M_{0\ ,n}-bar in terms of boundary strata.\n\nThis is joint work with Sean Griff in and Jake Levinson.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Vance Blankers (Northeastern University) DTSTART:20210916T163000Z DTEND:20210916T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/39 DESCRIPTION:Title: Alternative compactifications of the moduli space of curves\nby Vanc e Blankers (Northeastern University) as part of SFU NT-AG seminar\n\n\nAbs tract\nThe moduli space of curves is an important object in modern algebra ic geometry\, both interesting in its own right and serving as a test spac e for broader geometric programs. These often require the space to be comp act\, which leads to a variety of choices for compactification\, the most well-known of which is the Deligne-Mumford-Knudsen compactification by sta ble curves\, originally introduced in 1969. Since then\, several alternati ve compactifications have been constructed and studied\, and in 2013 David Smyth used a combinatorial framework to make progress towards classifying all "sufficiently nice" compactifications. In this talk\, I'll discuss so me of the most well-studied compactifications\, as well as two new compact ifications\, which together classify the Gorenstein compactifications in g enus 0 and genus 1.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Raymond Cheng (Columbia University) DTSTART:20211028T223000Z DTEND:20211028T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/40 DESCRIPTION:Title: Unbounded negativity on rational surfaces in positive characteristic \nby Raymond Cheng (Columbia University) as part of SFU NT-AG seminar\n\n\ nAbstract\nFix your favourite smooth projective surface S and wonder: 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 Conjecture\ , predicts that if S were defined over the complex numbers\, then the self -intersection of any curve in S is bounded below by a constant depending o nly on S. If\, however\, S were defined over a field of positive character istic\, then it is known that the Bounded Negativity Conjecture as stated cannot hold. For a long time\, however\, it was not known whether the Conj ecture failed for rational surfaces in positive characteristic. In this ta lk\, I describe the first examples of rational surfaces failing Bounded Ne gativity which I constructed with Remy van Dobben de Bruyn earlier this ye ar.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Shabnam Akhtari (University of Oregon) DTSTART:20211118T233000Z DTEND:20211119T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/41 DESCRIPTION:Title: Orders in cubic and quartic number fields and classical Diophantine equa tions\nby Shabnam Akhtari (University of Oregon) as part of SFU NT-AG seminar\n\n\nAbstract\nAn order $\\mathcal{O}$ in an algebraic number fiel d is called monogenic if over $\\mathbb{Z}$ it can be generated by one ele ment. Győry has shown that there are finitely equivalence classes $\\alph a \\in \\mathcal{O}$ such that $\\mathcal{O} = \\mathbb{Z}[\\alpha]$\, whe re two algebraic integers $\\alpha\, \\alpha'$ are called equivalent if $\ \alpha + \\alpha'$ or $\\alpha - \\alpha'$ is a rational integer. An inter esting problem is to count the number of monogenizations of a given monoge nic order. First we will note\, for a given order $\\mathcal{O}$\, that $$ \\mathcal{O} = \\mathbb{Z}[\\alpha] \\text{ in } \\alpha$$ is indeed a Dio phantine equation. Then we will discuss how some old algorithmic results c an be used to obtain new and improved upper bounds for the number of monog enizations of a cubic or quartic order.\n\nThis talk should be accessible to any math graduate student and\nquestions about basic concepts are welco me. We will start by recalling\nsome definitions from elementary algebraic number theory. Number\nfields\, lattices over $\\mathbb{Z}$\, and simple polynomial equations are the main\nfocus of this talk.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Escobar (Washington University in St. Louis) DTSTART:20211104T223000Z DTEND:20211104T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/42 DESCRIPTION:Title: Determining the complexity of Kazhdan-Lusztig varieties\nby Laura Es cobar (Washington University in St. Louis) as part of SFU NT-AG seminar\n\ n\nAbstract\nKazhdan-Lusztig varieties are defined by ideals generated by certain minors of a matrix\, which are chosen by a combinatorial rule. The se varieties are of interest in commutative algebra and Schubert varieties . Each Kazhdan-Lusztig variety has a natural torus action from which one c an construct a cone. The complexity of this torus action can be computed f rom the dimension of the cone and\, in some sense\, indicates how close th e variety is to the toric variety of the cone. In joint work with Maria Do nten-Bury and Irem Portakal we address the problem of classifying which Ka zhdan-Lusztig varieties have a given complexity. We do so by utilizing the rich combinatorics of Kazhdan-Lusztig varieties.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Habiba Kadiri (University of Lethbridge) DTSTART:20211021T223000Z DTEND:20211021T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/44 DESCRIPTION:Title: Primes in the Chebotarev density theorem for all number fields\nby H abiba Kadiri (University of Lethbridge) as part of SFU NT-AG seminar\n\nLe cture held in AQ 4145.\n\nAbstract\nLet $L/K$ be a Galois extension of num ber fields such that $L\\not=\\mathbb{Q}$\, and let $C$ be a conjugacy cla ss in the Galois group of $L/K$. We show that there exists an unramified p rime $\\mathfrak{p}$ of $K$ such that $\\sigma_{\\mathfrak{p}}=C$ and $N \ \mathfrak{p} \\le d_{L}^{B}$ with $B= 310$. This improves a previous resul t of Ahn and Kwon\, who showed that $B=12\\\,577$ is admissible. The main tool is a stronger Deuring-Heilbronn (zero-repulsion) phenomenon. We also use Fiori's numerical verification for a finite list of fields. This is jo int work with Peng-Jie Wong (NCTS\, Taiwan).\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabel Vogt (Brown University) DTSTART:20211209T233000Z DTEND:20211210T003000Z DTSTAMP:20260422T022949Z 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 o f genus g. A fundamental problem in the theory of algebraic curves is to u nderstand maps of C to projective space of dimension r of degree d. When t he curve C is general\, the moduli space of such maps is well-understood b y the main theorems of Brill--Noether theory. However\, in nature\, curve s C are often encountered already equipped with a map to some projective s pace\, which may force them to be special in moduli. The simplest case is when C is general among curves of fixed gonality. Despite much study ove r the past three decades\, a similarly complete picture has proved elusive in this case. In this talk\, I will discuss joint work with Eric Larson a nd 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://researchseminars.org/talk/SFUQNTAG/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Padmavathi Srinivasan (University of Georgia) DTSTART:20211202T233000Z DTEND:20211203T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/46 DESCRIPTION:Title: Some Galois cohomology classes arising from the fundamental group of a c urve\nby Padmavathi Srinivasan (University of Georgia) as part of SFU NT-AG seminar\n\n\nAbstract\nWe will first talk about the Ceresa class\, w hich is the image under a cycle class map of a canonical algebraic cycle a ssociated to a curve in its Jacobian. This class vanishes for all hyperell iptic curves and was expected to be nonvanishing for non-hyperelliptic cur ves. In joint work with Dean Bisogno\, Wanlin Li and Daniel Litt\, we cons truct a non-hyperelliptic genus 3 quotient of the Fricke-Macbeath curve wi th vanishing Ceresa class\, using the character theory of the automorphism group of the curve\, namely\, PSL_2(F_8). This will also include the tale of another explicit genus 3 curve studied by Schoen that was lost and the n found again!\n\nTime permitting\, we will also talk about some Galois co homology classes that obstruct the existence of rational points on curves\ , by obstructing splittings to natural exact sequences coming from the fun damental group of a curve. In joint work with Wanlin Li\, Daniel Litt and Nick Salter\, we use these obstruction classes to give a new proof of Grot hendieck’s section conjecture for the generic curve of genus g > 2. An a nalysis of the degeneration of these classes at the boundary of the moduli space of curves\, combined with a specialization argument lets us prove t he existence of infinitely many curves of each genus over p-adic fields an d number fields that satisfy the section conjecture.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (Simon Fraser University) DTSTART:20210923T223000Z DTEND:20210923T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/47 DESCRIPTION:Title: Cluster algebras and deformation theory\nby Nathan Ilten (Simon Fras er University) as part of SFU NT-AG seminar\n\n\nAbstract\nCluster Algebra s\, introduced in 2001 by Fomin and Zelevinsky\, are a kind of commutative ring equipped with special combinatorial structure. They appear in a rang e of contexts\, from representation theory to mirror symmetry. After provi ding a gentle introduction to cluster algebras\, I will report on one aspe ct of work-in-progress with Alfredo Nájera Chávez and Hipolito Treffinge r. We show that for cluster algebras of finite type\, the cluster algebra with universal coefficients is equal to a canonically identified subfamily of the semiuniversal family for the Stanley-Reisner ring of the cluster c omplex.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ng (University of Lethbridge) DTSTART:20211007T223000Z DTEND:20211007T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/51 DESCRIPTION:Title: Moments of the Riemann zeta function\nby Nathan Ng (University of Le thbridge) as part of SFU NT-AG seminar\n\n\nAbstract\nFor over a 100 years \, $I_k(T)$\, the $2k$-th moments of the Riemann zeta function on the crit ical line have been extensively studied. In 1918 Hardy-Littlewood establis hed an asymptotic formula for the second moment ($k=1$) and in 1926 Ingham established an asymptotic formula for the fourth moment $(k=2)$. Since th en no other moments have been asymptotically evaluated. In the late 1990' s Keating and Snaith gave a conjecture for the size of $I_k(T)$ based 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 ternary additive divisor sums. In this talk I will give an overview of these resu lts.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Klevdal (University of Utah) DTSTART:20211014T223000Z DTEND:20211014T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/52 DESCRIPTION:Title: Integrality of $G$-local systems\nby Christian Klevdal (University o f Utah) as part of SFU NT-AG seminar\n\n\nAbstract\nSimpson conjectured th at for a reductive group $G$\, rigid $G$-local systems on a smooth project ive complex variety are integral. I will discuss a proof of integrality fo r cohomologically rigid $G$-local systems. This generalizes and is inspire d by work of Esnault and Groechenig for $GL_n$. Surprisingly\, the main to ols used in the proof (for general $G$ and $GL_n$) are the work of L. Laff orgue on the Langlands program for curves over function fields\, and work of Drinfeld on companions of $\\ell$-adic sheaves. The major differences b etween 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://researchseminars.org/talk/SFUQNTAG/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricia Klein (University of Minnesota) DTSTART:20220113T233000Z DTEND:20220114T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/53 DESCRIPTION:Title: Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials\nby Patricia Klein (University of Minnesota) as part of SFU NT-AG semina r\n\n\nAbstract\nKnutson and Miller established a connection between the a nti-diagonal Gröbner degenerations of matrix Schubert varieties and the p re-existing combinatorics of pipe dreams. They used this correspondence to give a geometrically-natural explanation for the appearance of the combin atorially-defined Schubert polynomials as representatives of Schubert clas ses. In this talk\, we will describe a similar connection between diagonal degenerations of matrix Schubert varieties and bumpless pipe dreams\, new er combinatorial objects introduced by Lam\, Lee\, and Shimozono. This con nection was conjectured by Hamaker\, Pechenik\, and Weigandt. This talk is based on joint work with Anna Weigandt.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/53/ END:VEVENT BEGIN:VEVENT SUMMARY:José González (University of California\, Riverside) DTSTART:20220203T233000Z DTEND:20220204T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/56 DESCRIPTION:Title: Generation of jets and Fujita’s jet ampleness conjecture on toric vari eties\nby José González (University of California\, Riverside) as pa rt 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\, and also their higher order analogues called k-jets. For example\, 0-jet ampleness is equivalent to global generation and 1-jet ampleness is equivalent to v ery ampleness. We give sharp bounds guaranteeing that a line bundle on a p rojective toric variety is k-jet ample in terms of its intersection number s with the invariant curves\, in terms of the lattice lengths of the edges of its polytope\, in terms of the higher concavity of its piecewise linea r function and in terms of its Seshadri constant. As an application\, we p rove the k-jet generalizations of Fujita’s conjectures on toric varietie s.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Bryan (University of British Columbia) DTSTART:20220210T233000Z DTEND:20220211T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/57 DESCRIPTION:Title: Bott periodicity from algebraic geometry\nby Jim Bryan (University o f British Columbia) as part of SFU NT-AG seminar\n\n\nAbstract\nA famous t heorem in algebraic topology is Bott periodicity: the homotopy groups of t he 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 then I wil l explain how to formulate and prove a theorem in algebraic geometry which \, when specialized to the field of complex numbers\, recovers the usual t opological Bott periodicity\, but makes sense over any field. This is work in progress with Ravi Vakil.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Katrina Honigs (Simon Fraser University) DTSTART:20220217T233000Z DTEND:20220218T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/58 DESCRIPTION:Title: The fixed locus of a symplectic involution on a hyperkahler 4-fold of Ku mmer 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 involutions o f hyperkahler manifolds of Kummer type. The fixed loci of these involution s correspond to cohomology classes and have very interesting properties. T he talk will focus on the geometry of such a fixed locus on a particular 4 -fold.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Juliette Bruce (University of California\, Berkeley) DTSTART:20220303T233000Z DTEND:20220304T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/60 DESCRIPTION:Title: Multigraded regularity on products of projective spaces\nby Juliette Bruce (University of California\, Berkeley) as part of SFU NT-AG seminar\ n\n\nAbstract\nEisenbud and Goto described the Castelnuovo-Mumford regular ity of a module on projective space in terms of three different properties of the corresponding graded module: its betti numbers\, its local cohomol ogy\, and its truncations. For the multigraded generalization of regularit y defined by Maclagan and Smith\, these three conditions are no longer equ ivalent. I will characterize each of them for modules on products of proje ctive spaces.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Pietromonaco (University of British Columbia) DTSTART:20220324T223000Z DTEND:20220324T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/62 DESCRIPTION:Title: Enumerative Geometry of Orbifold K3 Surfaces\nby Stephen Pietromonac o (University of British Columbia) as part of SFU NT-AG seminar\n\nLecture held in K-9509.\n\nAbstract\nTwo of the most celebrated theorems in enume rative geometry\n(both predicted by string theorists) surround curve-count ing for K3\nsurfaces. The Yau-Zaslow formula computes the honest number 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 th is talk\, I will\nreview this story and then describe a recent generalizat ion to orbifold K3\nsurfaces. One interpretation of the new theory is as p roducing a virtual\ncount of curves in the orbifold\, where we track both the genus of the curve\nand the genus of the corresponding invariant curve upstairs. As one\nexample\, we generalize the counts of hyperelliptic cur ves in an Abelian\nsurface carried out by Bryan-Oberdieck-Pandharipande-Yi n. This is work in\nprogress with Jim Bryan.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Masahiro Nakahara (University of Washington) DTSTART:20220317T223000Z DTEND:20220317T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/63 DESCRIPTION:Title: Uniform potential density for rational points on algebraic groups and el liptic K3 surfaces\nby Masahiro Nakahara (University of Washington) as part of SFU NT-AG seminar\n\n\nAbstract\nA variety satisfies potential de nsity if it contains a dense subset of rational points after extending its ground field by a finite degree. A collection of varieties satisfies unif orm potential density if that degree can be uniformly bounded. I will disc uss this property for connected algebraic groups of a fixed dimension and elliptic K3 surfaces. This is joint work with Kuan-Wen Lai.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Marni Mishna (Simon Fraser University) DTSTART:20220331T223000Z DTEND:20220331T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/64 DESCRIPTION:Title: Lattice Walk Enumeration: Analytic\, algebraic and geometric aspects \nby Marni Mishna (Simon Fraser University) as part of SFU NT-AG seminar\n \nLecture held in K-9509.\n\nAbstract\nThis talk will survey classificatio n of lattice path models via their generating functions.. A very classic o bject of combinatorics\, lattice walks withstand study from a variety of p erspectives. Even the simple task of classifying the two dimensional neare st neighbour walks restricted to the first quadrant has brought into play a surprising diversity of techniques from algebra to analysis to geometry. We will consider walks under a few different lenses. We will see how latt ice walks can naturally guide the classification of functions into categor ies like algebraic\, D-finite\, differentiably algebraic and beyond. Elli ptic curves and differential Galois theory play an important role.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricia Klein (University of Minnesota) DTSTART:20220407T223000Z DTEND:20220407T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/65 DESCRIPTION:Title: Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials\nby Patricia Klein (University of Minnesota) as part of SFU NT-AG semina r\n\n\nAbstract\nKnutson and Miller established a connection between the a nti-diagonal Gröbner degenerations of matrix Schubert varieties and the p re-existing combinatorics of pipe dreams. They used this correspondence to give a geometrically-natural explanation for the appearance of the combin atorially-defined Schubert polynomials as representatives of Schubert clas ses. In this talk\, we will describe a similar connection between diagonal degenerations of matrix Schubert varieties and bumpless pipe dreams\, new er combinatorial objects introduced by Lam\, Lee\, and Shimozono. This con nection was conjectured by Hamaker\, Pechenik\, and Weigandt. This talk is based on joint work with Anna Weigandt.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Rohini Ramadas (Warwick Mathematics Institute) DTSTART:20220414T223000Z DTEND:20220414T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/66 DESCRIPTION:Title: The S_n action on the homology groups of M_{0\,n}-bar\nby Rohini Ram adas (Warwick Mathematics Institute) as part of SFU NT-AG seminar\n\n\nAbs tract\nThe moduli space M_{0\,n}-bar is a compactification of the space of configurations of n points on P^1. The symmetric group on n letters acts on M_{0\,n}-bar\, and thus on its (co-)homology groups. I will introduce M _{0\,n}-bar\, its (co-)homology groups\, and the S_n action. This talk inc ludes joint work with Rob Silversmith.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/66/ END:VEVENT BEGIN:VEVENT SUMMARY:NTAG faculty DTSTART:20220915T223000Z DTEND:20220915T233000Z DTSTAMP:20260422T022949Z 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 faculty. We'll each say a bit about our areas of interest within algebraic geometry and/or number theory.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Lena Ji (University of Michigan) DTSTART:20220922T223000Z DTEND:20220922T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/69 DESCRIPTION:Title: Rationality of conic bundle threefolds over non-closed fields\nby Le na Ji (University of Michigan) as part of SFU NT-AG seminar\n\n\nAbstract\ nClemens–Griffiths introduced the classical intermediate Jacobian obstru ction to rationality for complex threefolds\, and used it to show irration ality of the cubic threefold. Recently\, over non-closed fields\, Hassett –Tschinkel and Benoist–Wittenberg refined this obstruction using torso rs over the intermediate Jacobian. In this talk\, we identify these interm ediate Jacobian torsors for conic bundle threefolds\, and we give applicat ions to rationality over non-closed fields. This talk is based on joint wo rk with S. Frei\, S. Sankar\, B. Viray\, and I. Vogt\, and on joint work w ith M. Ji.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Bruin (Simon Fraser University) DTSTART:20220929T223000Z DTEND:20220929T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/70 DESCRIPTION:Title: Twists of the Burkhardt quartic threefold\nby Nils Bruin (Simon Fras er 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 ellipti c curves:\n\\[x^3+y^3+z^3+ \\lambda xyz = 0\,\\]\nwhich gives a family of elliptic curves with labelled 3-torsion points. The parameter $\\lambda$ i s a parameter on the corresponding moduli space.\n\nThe analogue for genus 2 curves is given by the Burkhardt quartic threefold. In this talk\, we w ill go over some of its interesting geometric properties. In an arithmetic context\, where one considers a non-algebraically closed base field\, it is also important to consider the different possible twists of th e space. We will discuss an interesting link with a so-called field of definition obstruction that occurs for genus 2 curves\, and see that this obstruction has interesting consequences for the existence of ration al points on certain twists of the Burkhardt quartic.\n\nThis talk is base d on joint works with my students Brett Nasserden and Eugene Filatov.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Nahid Walji (University of British Columbia) DTSTART:20221006T230000Z DTEND:20221007T000000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/71 DESCRIPTION:Title: Distribution of traces of Frobenius and the Lang-Trotter conjecture on a verage for families of elliptic curves\nby Nahid Walji (University 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 traces o f Frobenius for various families of elliptic curves with respect to the La ng--Trotter conjecture and extremal primes. These are related to the work of Sha--Shparlinski on the average Lang--Trotter conjecture for single-par ametric families as well as the work of various authors on the distributio n of traces of Frobenius for primes in congruence classes. This is joint w ork with my former student Nathan Fugleberg.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhe Xu (Simon Fraser University) DTSTART:20221013T223000Z DTEND:20221013T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/72 DESCRIPTION:Title: On the local behaviour of symmetric differentials on the blow-up of Du V al singularities\nby Zhe Xu (Simon Fraser University) as part of SFU N T-AG seminar\n\nLecture held in K-9509.\n\nAbstract\nDu Val singularities appear in the classification of algebraic surfaces and other areas of alge braic geometry. Wahl's concept of local Euler characteristics of sheaves h elps in describing the properties of these singularities. We consider the sheaf of symmetric differentials and compute one ingredient of the local E uler characteristic: the codimension of those symmetric differentials that extend to the blow-up of the singularity in the space of those that are r egular around it. For singularities of type \\(A_n\\)\, we show that this codimension can be expressed combinatorially as a lattice point count in a polytope. Ehrhart's quasi-polynomials allow us to find closed expressions for this codimension as a function of the symmetric differential degree. We expect our method to generalize to all Du Val singularities.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Kristin DeVleming (University of Massachusetts\, Amherst) DTSTART:20221020T223000Z DTEND:20221020T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/73 DESCRIPTION:Title: A question of Mori and families of plane curves\nby Kristin DeVlemin g (University of Massachusetts\, Amherst) as part of SFU NT-AG seminar\n\n \nAbstract\nConsider a smooth family of hypersurfaces of degree d in 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 ans wer is "no" when the degree d is composite\, there are no known examples w hen d is prime and n>2! We will pose this as a conjecture (primality of d egree is sufficient to ensure every smooth limit is a hypersurface\, for n > 2). However\, there are counterexamples when n=1 or 2. In this talk\, w e will propose a re-formulation of the conjecture that explains the failur e in low dimensions\, provide results in dimension one\, and discuss a gen eral approach to the problem using moduli spaces of pairs. This is joint w ork with David Stapleton.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Brooke (University of Oregon) DTSTART:20221027T223000Z DTEND:20221027T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/74 DESCRIPTION:Title: Abelian surface fibrations and lines on cubic fourfolds\nby Corey Br ooke (University of Oregon) as part of SFU NT-AG seminar\n\n\nAbstract\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 of dimen sion four. Over the complex numbers\, tools from hyperkähler geometry rev eal that F only admits a nontrivial morphism to a lower-dimensional variet y when X contains certain "special" algebraic surfaces. In this talk\, we consider the case when X contains a plane: it turns out that F is biration al to another irreducible symplectic variety admitting a morphism to P^2 w hose general fiber is an abelian surface. We will show the key geometric i ngredients involved in this construction and describe some of its arithmet ic when the ground field is not closed.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Catherine Cannizzo (University of California\, Riverside) DTSTART:20221103T223000Z DTEND:20221103T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/75 DESCRIPTION:Title: Homological Mirror Symmetry for Theta Divisors\nby Catherine Cannizz o (University of California\, Riverside) as part of SFU NT-AG seminar\n\n\ nAbstract\nMirror symmetry relates complex and symplectic manifolds which come in mirror pairs\, and homological mirror symmetry is an equivalence o f categories on each. In forthcoming joint work with Haniya Azam\, Heather Lee\, and Chiu-Chu Melissa Liu\, we prove a global homological mirror sym metry result for genus 2 curves. We consider genus 2 curves as hypersurfac es of principally polarized abelian surfaces\, on the complex side. In a f ollow-up paper\, we allow the abelian variety to have arbitrary dimension\ , and hypersurfaces are now theta divisors. This talk will overview the re sults of these papers.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Topaz (University of Alberta) DTSTART:20221110T233000Z DTEND:20221111T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/76 DESCRIPTION:Title: An overview of the liquid tensor experiment\nby Adam Topaz (Universi ty of Alberta) as part of SFU NT-AG seminar\n\nLecture held in K-9509.\n\n Abstract\nIn December 2020\, Peter Scholze proposed a challenge to formall y verify a theorem he and Dustin Clausen proved about the real numbers in the context of condensed mathematics\, saying it might be his "most import ant theorem to date." I was part of the group who took on this challenge\, using the Lean3 interactive theorem prover and its formally verified math ematics library `mathlib`. We completed the challenge in July 2022. In thi s talk\, I will give a broad overview of condensed/liquid mathematics and the corresponding formalization in Lean. No background in condensed mathem atics or interactive theorem provers will be necessary for this talk.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Imin Chen (Simon Fraser University) DTSTART:20221117T233000Z DTEND:20221118T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/77 DESCRIPTION:Title: A multi-Frey approach to Fermat equations of signature (11\,11\,n)\n by Imin Chen (Simon Fraser University) as part of SFU NT-AG seminar\n\nLec ture held in K-9509.\n\nAbstract\nI will report on joint work with Billere y\, Dieulefait\, Freitas\, and Najman in which we develop some of the nece ssary ingredients to use Frey abelian varieties in the modular method\, in spired by ideas from Darmon's program for resolving generalized Fermat equ ations. In particular\, I will explain how this machinery can be applied t o study the equation x^11 + y^11 = z^n for first case solutions by using i nformation from multiple Frey varieties.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Tyler Kelly (University of Birmingham) DTSTART:20221124T233000Z DTEND:20221125T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/78 DESCRIPTION:Title: Open Mirror Symmetry for Landau-Ginzburg models\nby Tyler Kelly (Uni versity of Birmingham) as part of SFU NT-AG seminar\n\nLecture held in K-9 509.\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-p rojective variety $X$ with a group $G$ acting on $X$ leaving $W$ invariant . One can build an analogue of Hodge theory and period integrals associate d to an LG model when $G$ is trivial. This involves oscillatory integrals on certain cycles in\n$X$ (fear not: this is actually cute and will be don e in examples!). Mirror symmetry states that period integrals often encode enumerative geometry and this is also the case here. An\nenumerative theo ry developed by Fan\, Jarvis\, and Ruan gives FJRW invariants\, the analog ue of Gromov-Witten invariants for LG models. These invariants are now cal led FJRW invariants. A problem is that finding the right deformation perio d integrals is hard. We define and use a new open enumerative theory for c ertain Landau-Ginzburg LG models to solve this problem in low dimension. \ n\nRoughly speaking\, this involves computing specific integrals on certai n moduli of disks with boundary and interior marked points. One can then c onstruct a mirror Landau-Ginzburg model to a Landau-Ginzburg model using t hese 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 ma nifolds. This is joint work with Mark Gross and Ran Tessler.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Yixin Chen (Simon Fraser University) DTSTART:20221201T233000Z DTEND:20221202T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/79 DESCRIPTION:Title: Two-torsion of the Brauer Group of an Elliptic Surface\nby Yixin Che n (Simon Fraser University) as part of SFU NT-AG seminar\n\nLecture held i n K-9509.\n\nAbstract\nThe Brauer group of a variety encodes important ari thmetic information. For instance\, it plays an important role in the Brau er-Manin obstruction\, which governs the existence of rational points on m any varieties. In this thesis we describe the 2-torsion part of the Brauer group of certain elliptic surfaces. In particular\, we compute explicit r epresentatives of these elements in terms of quaternion algebras over the function field of the surface.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Sho Tanimoto (Nagoya University) DTSTART:20221206T233000Z DTEND:20221207T003000Z DTSTAMP:20260422T022949Z 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\nAbs tract\nManin’s conjecture is a conjectural asymptotic formula for the co unting function of rational points on Fano varieties over global fields. M ainly with Brian Lehmann\, I have been studying exceptional sets arising i n this conjecture. In this talk I would like to discuss my joint work with Brian Lehmann and Akash Sengupta on birational geometry of exceptional se ts\, then I will discuss applications of this study to understand the geom etry of moduli spaces of sections on Fano fibrations which is joint work w ith Brian Lehmann and Eric Riedl.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Catherine Hsu (Swarthmore College) DTSTART:20230216T233000Z DTEND:20230217T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/81 DESCRIPTION:Title: Explicit non-Gorenstein R=T via rank bounds\nby Catherine Hsu (Swart hmore College) as part of SFU NT-AG seminar\n\nLecture held in K-9509.\n\n Abstract\nIn his seminal work on modular curves and the Eisenstein ideal\, Mazur studied the existence of congruences between certain Eisenstein ser ies and newforms\, proving that Eisenstein ideals associated to weight 2 c usp forms of prime level are locally principal. In this talk\, we'll explo re generalizations of Mazur's result to squarefree level\, focusing on rec ent work\, joint with P. Wake and C. Wang-Erickson\, about a non-optimal l evel N that is the product of two distinct primes and where the Galois def ormation ring is not expected to be Gorenstein. First\, we will outline a Galois-theoretic criterion for the deformation ring to be as small as poss ible\, and when this criterion is satisfied\, deduce an R=T theorem. Then we'll discuss some of the techniques required to computationally verify th e criterion.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/81/ END:VEVENT BEGIN:VEVENT SUMMARY:June Park (University of Melbourne) DTSTART:20230126T233000Z DTEND:20230127T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/82 DESCRIPTION:Title: Space of morphisms & Moduli stack of elliptic fibrations\nby June Pa rk (University of Melbourne) as part of SFU NT-AG seminar\n\n\nAbstract\nT he defining property of fine moduli stacks (of curves) is that they have ' universal families' which translates the study of a family of (curves) as the study of morphisms to moduli stacks. I will explain this idea using Ho m_{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 a rithmetic invariants via topological methods.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/82/ END:VEVENT BEGIN:VEVENT SUMMARY:(reading break) DTSTART:20230223T233000Z DTEND:20230224T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/83 DESCRIPTION:by (reading break) as part of SFU NT-AG seminar\n\nAbstract: T BA\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Inchiostro (University of Washington) DTSTART:20230323T223000Z DTEND:20230323T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/84 DESCRIPTION:Title: Wall crossing morphisms for moduli of stable pairs\nby Giovanni Inch iostro (University of Washington) as part of SFU NT-AG seminar\n\nLecture held in AQ 4140.\n\nAbstract\nConsider a quasi-compact moduli space M of p airs (X\,D) consisting of a variety X and a divisor D on X. If M is not pr oper\, it is reasonable to find a compactification of it. Assume furthermo re 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 construct 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 a re birational morphisms $M_a \\to M_b$\, recovering Hassett's result (for the case of curves) in all dimensions. If time permits\, I will explain a slight variation of the moduli functor of varieties with pairs\, which has a particularly accessible moduli functor\, leads to a simple proof of the projectivity of the moduli of stable pairs\, and conjecturally leads to b etter wall-crossing phenomena. The talk will be based on my work with Kenn y Ascher\, Dori Bejleri\, Zsolt Patakfalvi\; and my work with Stefano Fili pazzi.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Jen Paulhus (Grinnell College) DTSTART:20230330T223000Z DTEND:20230330T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/85 DESCRIPTION:Title: (postponed) Automorphism groups of Riemann surfaces\nby Jen Paulhus (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 surfac es 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 R iemann-Hurwitz formula gives us an expectation for when a particular group should be the automorphism group of a Riemann surface of a particular gen us. 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 id eas in the field\, explain the connection with curves over number fields\, and talk about recent results to classify groups which are indeed automor phisms in just about every genus they should be. We’ll also make a surp rising connection to simple groups.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Ahmad Mokhtar (Simon Fraser University) DTSTART:20230202T233000Z DTEND:20230203T003000Z DTSTAMP:20260422T022949Z 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 linear spa ces contained in an embedded projective variety. In this talk\, I investig ate the Fano schemes parameterizing linear subspaces of symmetric matrices whose elements are all singular. I discuss their irreducibility\, smoothn ess\, and connectedness and show that they can have generically non-reduce d components. As an application\, I outline how to use the geometry of the se schemes to give alternative arguments for several results on subspaces of singular symmetric matrices.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Eva-Marie Hainzl (TU Wien) DTSTART:20230209T233000Z DTEND:20230210T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/87 DESCRIPTION:Title: Universal types of singularities of solutions to functional equation sys tems\nby Eva-Marie Hainzl (TU Wien) as part of SFU NT-AG seminar\n\nLe cture held in K-9509.\n\nAbstract\nDecompositions of combinatorial structu res translate very often to functional equations with positive coefficient s for their generating functions. A theorem by Bender says that if the gen erating function is univariate and the equation not linear\, the generatin g function always has a dominant square root singularity - which in turn m eans 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 str ongly connected finite systems of equations\, but as the system becomes in finite we can observe a broader variety of singularities appearing. \nIn t his talk\, I will give an overview of functional equations systems and the ir singular behaviour in combinatorics and present some recent results on universal types of singularities of solutions to infinite systems which co llapse to a single equation by introducing a second (catalytic) variable.\ n LOCATION:https://researchseminars.org/talk/SFUQNTAG/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Yifeng Huang (University of British Columbia) DTSTART:20230302T233000Z DTEND:20230303T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/88 DESCRIPTION:Title: Matrix points on varieties and punctual Hilbert (and Quot) schemes\n by Yifeng Huang (University of British Columbia) as part of SFU NT-AG semi nar\n\nLecture held in K-95095.\n\nAbstract\nModuli spaces often have inte resting enumerative properties. The goal of this talk is to introduce some enumerative results on solutions of matrix equations and zero-dimensional sheaves over singular curves. To motivate them\, I first discuss several moduli spaces in general\, which I put onto the "unframed" side and the "f ramed" side. The unframed side includes the commuting variety AB=BA of n x n matrices\, the variety of commuting matrices satisfying polynomial equa tions (the titular "matrix points on varieties")\, and the moduli stack of zero-dimensional coherent sheaves on a variety. The framed side includes the Hilbert scheme of points on a variety\, or more generally\, the Quot s cheme of zero-dimensional quotients of a vector bundle on a variety. The e numerative properties to be considered are point counts over finite fields and the motive in the Grothendieck ring of varieties\, which essentially keep track of the combinatorial data of a stratification of the space in q uestion. I will explain some general connections within and between the tw o sides\, and known results for smooth curves and smooth surfaces. Finally \, I will discuss recent results on singular curves. This talk is based on joint work with Ruofan Jiang.\n\nIn the pre-seminar\, I plan to talk abou t a super fun combinatorial construction\, which we call “spiral shiftin g operators”\, used in the proof of one of our results.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Sharon Robins (Simon Fraser University) DTSTART:20230309T233000Z DTEND:20230310T003000Z DTSTAMP:20260422T022949Z 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 held 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 infinites imal methods\, studying possible obstructions\, and attempting to construc t a family called a versal deformation\, which collects all possible defor mations. If X is a smooth projective toric variety\, combinatorial descrip tions of the space of first-order deformations and the obstruction to seco nd-order deformation given by the cup product have been studied. In this t alk\, I will present these descriptions with an example of a smooth projec tive toric threefold with a quadratic obstruction. In addition\, I will di scuss my current research\, which provides a combinatorial iterative proce dure for finding higher-order obstructions.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Susan Cooper (University of Manitoba) DTSTART:20230317T223000Z DTEND:20230317T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/90 DESCRIPTION:Title: Limiting Behaviour of Symbolic Powers\nby Susan Cooper (University o f Manitoba) as part of SFU NT-AG seminar\n\nLecture held in AQ 4120.\n\nAb stract\nAt the heart of many problems in Commutative Algebra and Algebraic Geometry is the difference between symbolic and regular powers of a homog eneous ideal. One way to find failures of containments between these power s is to use an asymptotic approach and look at a special limit called the Waldschmidt constant. This limit was first introduced as a way to estimate the lowest degree of a hypersurface vanishing at all the points of a vari ety to a given order. However\, this limit is challenging to compute and s o it is natural to focus our attention on special ideals to gain insight. In this talk we will give some interpretations of the Waldschmidt constan t of a monomial ideal which allow us to determine this limit in a number o f cases. This is joint work from two projects: the first with R. Embree\, H. T. Hà\, and A. Hoefel and the second with C. Bocci\, E. Guardo\, B. Ha rbourne\, M. Janssen\, U. Nagel\, A. Seceleanu\, A. Van Tuyl\, and T. Vu.\ n LOCATION:https://researchseminars.org/talk/SFUQNTAG/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandru Constantinescu (Freie Universität Berlin) DTSTART:20230331T223000Z DTEND:20230331T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/91 DESCRIPTION:Title: Cotangent Cohomology for Matroids\nby Alexandru Constantinescu (Frei e Universität Berlin) as part of SFU NT-AG seminar\n\nLecture held in 3:3 0-4:20.\n\nAbstract\nThe first cotangent cohomology module $T^1$ describes the first order deformations of a commutative ring. For Stanley-Reisner r ings\, this module has a purely combinatorial description: its multigraded components are given as the relative cohomology of some topological space s associated to the defining simplicial complex. When the Stanley-Reisner ring is associated to a matroid\, I will present a very explicit formula f or the dimensions of these components. Furthermore\, I will show that $T^1 $ provides a new complete characterization for matroids.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Katz (California State University\, Northridge) DTSTART:20230809T173000Z DTEND:20230809T183000Z DTSTAMP:20260422T022949Z 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 semi nar\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 field\, $\\ psi$ is the canonical additive character of \n$F$\, the coefficient $a$ is a nonzero element of $F$\, and $d$ is a \npositive integer such that $\\g cd(d\,|F|-1)=1$. This last condition makes \n$x\\mapsto x^d$ a power perm utation of $F$\, that is\, a power map that \npermutes $F$. These Weil su ms 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 We il 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 b inomial of the form $x^d-a x$ are used \nto count points on varieties over finite fields\, and have multiple \napplications to cryptography and comm unications. Since one sums roots \nof unity in the complex plane to obtai n the Weil spectrum values\, these \nare always algebraic integers. A rat ional Weil spectrum is one whose \nvalues are all rational integers. If o ne sets aside degenerate cases\, \nHelleseth showed that Weil spectra have at least three distinct values. \nIt has been shown that all spectra with exactly three distinct values \nare rational. In this talk\, we show tha t\, with one exception\, Weil \nspectra with exactly four distinct values are also always rational. \nThis is joint work with Allison E.\\ Wong\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/92/ END:VEVENT BEGIN:VEVENT SUMMARY:All NTAG faculty and students DTSTART:20230907T223000Z DTEND:20230907T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/93 DESCRIPTION:Title: How to NTAG...get the most out of the seminar!\nby All NTAG faculty and students as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Zotine (Queen's University) DTSTART:20230914T223000Z DTEND:20230914T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/94 DESCRIPTION:Title: Computing Higher Direct Images of Toric Morphisms\nby Alexandre Zoti ne (Queen's University) as part of SFU NT-AG seminar\n\n\nAbstract\nSheaf cohomology is a ubiquituous tool in algebraic geometry for understanding t he structure of varieties---but how does one actually get one's hands on c ohomology? In this talk\, I will discuss computing sheaf cohomology (and h igher direct images) of toric varieties\, which translate geometry into co mbinatorics. This translation is far more accessible and amenable to compu tation\, allowing us to get a more tangible grasp of the abstract construc tions. In particular\, I implemented an algorithm for computing the higher direct images of toric morphisms for line bundles in Macaulay2\, which I will demonstrate. This is joint work with Mike Roth and Greg Smith.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Shoemaker (Colorado State) DTSTART:20231130T233000Z DTEND:20231201T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/95 DESCRIPTION:Title: Counting curves in quiver varieties\nby Mark Shoemaker (Colorado Sta te) as part of SFU NT-AG seminar\n\n\nAbstract\nFrom a directed graph $Q$\ , called a quiver\, one can construct what is known as a quiver variety $Y _Q$\, an algebraic variety defined as a quotient of a vector space by a gr oup defined in terms of $Q$. A mutation of a quiver is an operation that produces from $Q$ a new directed graph $Q’$ and a new associated quiver variety $Y_{Q’}$. Quivers and mutations have a number of connections to representation theory\, combinatorics\, and physics. The mutation conjec ture predicts a surprising and beautiful connection between the number of curves in $Y_Q$ and the number in $Y_{Q’}$. In this talk I will describ e quiver varieties and mutations\, give some examples to convince you that you’re already well-acquainted with some quiver varieties and their mut ations\, and discuss an application to the study of determinantal varietie s. This is based on joint work with Nathan Priddis and Yaoxiong Wen.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Jen Paulhus (Grinnell College) DTSTART:20231012T223000Z DTEND:20231012T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/96 DESCRIPTION:Title: Automorphism groups of Riemann surfaces\nby Jen Paulhus (Grinnell Co llege) as part of SFU NT-AG seminar\n\n\nAbstract\nA well-known result on compact Riemann surfaces says that the automorphism group of any such surf ace is a finite group of bounded size (based on the genus of the surface). Additionally\, the Riemann-Hurwitz formula gives us an expectation for wh en a particular group should be the automorphism group of a Riemann surfac e of a particular genus. There has been a lot of work over the last 20 yea rs 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 curve s over number fields\, and talk about recent results to classify groups wh ich are indeed automorphisms in just about every genus they should be. We ’ll also make a surprising connection to simple groups.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Ursula Whitcher (AMS) DTSTART:20231123T233000Z DTEND:20231124T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/97 DESCRIPTION:Title: Adinkra heights and color-splitting rainbows\nby Ursula Whitcher (AM S) as part of SFU NT-AG seminar\n\n\nAbstract\nAdinkras are decorated grap hs that encapsulate information about conjectural relationships between fu ndamental 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 structure to characterize height functions on Adinkras with five colors\, then show how to compute the same information using data from our rainbow. This tal k describes joint work with Amanda Francis.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Emiel Haakma (SFU) DTSTART:20231019T230000Z DTEND:20231020T000000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/98 DESCRIPTION:Title: A method of 2-descent on a genus 3 hyperelliptic curve\nby Emiel Haa kma (SFU) as part of SFU NT-AG seminar\n\n\nAbstract\nThe rational points of an abelian variety form a finitely generated group and computing the r ank of this group is a hard and central problem in arithmetic geometry. On e method\, which follows the original proof of Mordell and Weil of the fin iteness of this rank\, is explicit finite descent. It approximates it usin g Selmer groups\, which bounds the rank using local information. The Tate- Shafarevich group measures the failure of this bound to be sharp. It is on e of the most mysterious objects in arithmetic geometry.\n\nTate-Shafarevi ch groups have been shown to grow arbitrarily large in certain families by comparing different but related Selmer groups. Results on this have been primarily for Jacobians of hyperelliptic and superelliptic curves\, which have additional automorphisms.\n\nWe discuss generalizations of these meth ods to curves of genus 3\, which has the important distinction that not al l curves are hyperelliptic. This will give us computational access to vari ous Selmer groups of abelian threefolds with minimal endomorphism ring and that are not hyperelliptic Jacobians\, and potentially allow us to show t hat the 2-torsion of Tate-Shafarevich groups for them is unbounded.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Jake Levinson (Université de Montréal) DTSTART:20231026T223000Z DTEND:20231026T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/99 DESCRIPTION:Title: Minimal degree fibrations in curves and asymptotic degrees of irrational ity\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 ho w similar it is to projective space. One measure of similarity is the mini mum degree of a rational map from X to projective space\, the "degree of i rrationality". This number\, not to mention the corresponding minimal-degr ee maps\, is in general challenging to compute\, but captures special feat ures of the geometry of X. I will discuss some recent joint work with Davi d Stapleton and Brooke Ullery on asymptotic bounds for degrees of irration ality of divisors X on projective varieties Y. Here\, the minimal-degree r ational maps $X \\dashrightarrow \\mathbb{P}^n$ turn out to "know" about Y and factor through rational maps $Y \\dashrightarrow \\mathbb{P}^n$ fiber ed in curves that are\, in an appropriate sense\, also of minimal degree.\ n LOCATION:https://researchseminars.org/talk/SFUQNTAG/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Meazinni (Bologna) DTSTART:20231109T233000Z DTEND:20231110T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/100 DESCRIPTION:Title: On some formality problems in deformation theory\nby Francesco Meaz inni (Bologna) as part of SFU NT-AG seminar\n\n\nAbstract\nI will briefly introduce the notion of formality for differential graded Lie algebras\, a nd the role it plays in deformation theory. I will then discuss some geome tric applications obtained in a joint work with Claudio Onorati.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Petracci (Bologna) DTSTART:20231102T223000Z DTEND:20231102T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/101 DESCRIPTION:Title: Moduli spaces of Fano varieties can be singular\nby Andrea Petracci (Bologna) as part of SFU NT-AG seminar\n\n\nAbstract\nFano varieties are projective algebraic variety with “positive curvature”. Recently\, usi ng the notion of K-stability which originates in differential geometry\, p rojective moduli spaces for Fano varieties have been constructed. In this talk I will show how to use polytopes and toric geometry (which is the stu dy of certain algebraic varieties constructed in a combinatorial fashion) to produce singular points on these moduli spaces of Fano varieties. The t alk is based on joint work with Anne-Sophie Kaloghiros.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Bragg (Utah) DTSTART:20231116T233000Z DTEND:20231117T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/102 DESCRIPTION:Title: Murphy's Law for the stack of curves\nby Daniel Bragg (Utah) as par t of SFU NT-AG seminar\n\n\nAbstract\nWhen trying to classify curves over a non-algebraically closed field\, one quickly runs into the difficulty th at there are curves which are not defined over their fields of moduli. We will explain what this means with some examples. We will discuss how this phenomenon can be thought of geometrically in the moduli space of curves\, using residual gerbes. We will then explain some recent work with Max Lie blich on solving the corresponding inverse problem: specifically\, we show that every Deligne-Mumford gerbe over a field occurs as the residual gerb e of a point of the moduli stack of curves. This means that every possible way that a curve could fail to be defined over its field of moduli actual ly does occur\, that is\, everything that could go wrong does.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Bruin (SFU) DTSTART:20230928T223000Z DTEND:20230928T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/103 DESCRIPTION:Title: Jacobians of genus 4 curves that are (2\,2)-decomposable\nby Nils B ruin (SFU) as part of SFU NT-AG seminar\n\n\nAbstract\nDecomposable abelia n varieties\, and particularly decomposable Jacobians\, have a long histor y\; mainly in the form of formulas to compute hyperelliptic integrals in t erms of elliptic ones.\n\nThe first case where one can have a decomposable Jacobian without elliptic factors is for genus 4: one could have one that is isogenous to the product of two genus 2 Jacobians. Interestingly\, tho ugh\, not all four-dimensional abelian varieties (not even the principally polarized ones) are Jacobians. Classifying which genus 2 Jacobians can be glued together to yield a Jacobian of a genus 4 curve leads to some very interesting geometry on the Castelnuovo-Richmond-Igusa quartic threefold. We will introduce the requisite geometry and sketch some interesting resul ts that follow.\n\nThis is joint work with Avinash Kulkarni.\n\nThere will be an informal pre-seminar for graduate students at 3pm.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/103/ END:VEVENT BEGIN:VEVENT SUMMARY:TBD DTSTART:20240118T233000Z DTEND:20240119T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/105 DESCRIPTION:by TBD as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Debaditya Raychaudhury (University of Arizona) DTSTART:20240125T233000Z DTEND:20240126T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/106 DESCRIPTION:Title: On the singularities of secant varieties\nby Debaditya Raychaudhury (University of Arizona) as part of SFU NT-AG seminar\n\n\nAbstract\nIn th is talk\, we study the singularities of secant varieties of smooth project ive varieties when the embedding line bundle is sufficiently positive. We give a necessary and sufficient condition for these to have p-Du Bois sing ularities. In addition\, we show that the singularities of these varieties are never higher rational. From our results\, we deduce several consequen ces\, including a Kodaira-Akizuki-Nakano type vanishing result for the ref lexive differential forms of the secant varieties. Work in collaboration w ith S. Olano and L. Song.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/106/ END:VEVENT BEGIN:VEVENT SUMMARY:TBD DTSTART:20240201T233000Z DTEND:20240202T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/107 DESCRIPTION:by TBD as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Williams (UBC) DTSTART:20240208T233000Z DTEND:20240209T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/108 DESCRIPTION:Title: Extraordinary involutions on Azumaya algebras\nby Ben Williams (UBC ) as part of SFU NT-AG seminar\n\n\nAbstract\nThis is joint work with Uriy a First. If $R$ is a ring and $n$ is a natural number\, then an Azumaya al gebra of degree $n$ on $R$ is an $R$-algebra such that $A$ becomes isomorp hic to the $n \\times n$ matrix algebra after some faithfully flat extensi on of scalars. An involution of an Azumaya algebra is an additive self map of order $2$ that reverses the multiplication. One obtains examples of Az umaya algebras with involution by starting with a projective $R$-module $P $ of rank $n$\, equipped with a hermitian form. The endomorphism ring $\\E nd_R(P)$ has the structure of an Azumaya algebra with involution. One may even allow the hermitian form to take values in a rank-$1$ projective $R$- module\, rather than in $R$ itself.\n\nWe will say that an Azumaya algebra with involution $(A\, \\sigma)$ is semiordinary if there it becomes isomo rphic to one constructed from a hermitian form after a faithfully flat ext ension of scalars. Although this is an extremely broad class of Azumaya al gebras with involution\, I will show that it is not all of them: there exi st Azumaya algebras with truly extraordinary involutions. The method is to find an obstruction to being semiordinary in equivariant algebraic topolo gy.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter McDonald (University of Utah) DTSTART:20240215T233000Z DTEND:20240216T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/109 DESCRIPTION:Title: Splinter-type conditions for classifying singularities\nby Peter Mc Donald (University of Utah) as part of SFU NT-AG seminar\n\n\nAbstract\nTh e Direct Summand Theorem states that if $R$ is a commutative Noetherian ri ng\, then any finite extension $R\\to S$ splits as a map of $R$-modules. T his 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 map $\\pi :Y\\to X$ 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 the hist ory of using splinter-type conditions to classify singularities\, includin g work of Bhatt and Kov\\'acs\, with the goal of introducing a recent resu lt giving a splinter-type characterization of klt singularities.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Haggai Liu (Simon Fraser University) DTSTART:20240229T233000Z DTEND:20240301T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/110 DESCRIPTION:Title: Moduli Spaces of Weighted Stable Curves and their Fundamental Groups\nby Haggai Liu (Simon Fraser University) as part of SFU NT-AG seminar\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 exampl e\, it is a smooth projective variety over its base field. Many interestin g properties are known for the manifold $\\overline{M_{0\,n}}(\\mathbb{R}) $ of real points of this variety. In particular\, its fundamental group\, $\\pi_1(\\overline{M_{0\,n}}(\\mathbb{R}))$\, is related\, via a short exa ct sequence\, to another group known as the cactus group. Henriques and Ka mnitzer gave an elegant combinatorial presentation of this cactus group.\n \nIn 2003\, Hassett constructed a weighted variant 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 fundamen tal groups of Hassett spaces with certain restrictions on the weights. \n In particular\, we express the Hassett space as a blow-down of $\\o verline{M_{0\,n}}$ and modify the cactus group to produce an analogous sho rt exact sequence. The relations of this modified cactus group involves ex tensions to the braid relations in $S_n$. To establish the sufficiency of such relations\, we consider a certain cell decomposition of these Hassett spaces\, which are indexed by ordered planar trees.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/110/ END:VEVENT BEGIN:VEVENT SUMMARY:TBD DTSTART:20240307T233000Z DTEND:20240308T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/111 DESCRIPTION:by TBD as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Farbod Shokrieh (University of Washington) DTSTART:20240314T223000Z DTEND:20240314T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/112 DESCRIPTION:Title: Heights\, abelian varieties\, and tropical geometry\nby Farbod Shok rieh (University of Washington) as part of SFU NT-AG seminar\n\n\nAbstract \nI will describe some connections between arithmetic geometry of abelian varieties\, non-archimedean/tropical geometry\, and combinatorics. For a p rincipally polarized abelian variety\, we show an identity relating the Fa ltings height and the Néron--Tate height (of a symmetric effective diviso r defining the polarization) which involves invariants arising from non-ar chimedean/tropical geometry. If time permits\, we also give formulas for ( non archimedean) canonical local heights in terms of tropical invariants. (Based on joint work with Robin de Jong)\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Kyle Yip (UBC) DTSTART:20240321T223000Z DTEND:20240321T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/113 DESCRIPTION:Title: Diophantine tuples and bipartite Diophantine tuples\nby Kyle Yip (U BC) as part of SFU NT-AG seminar\n\n\nAbstract\nA set of positive integers is called a Diophantine tuple if the product of any two distinct elements in the set is one less than a square. There is a long history and extensi ve literature on the study of Diophantine tuples and their generalizations in various settings. In this talk\, we focus on the following generalizat ion: for integers $n \\neq 0$ and $k \\ge 3$\, we call a set of positive i ntegers 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 denote $M_ k(n)$ 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 bipart ite analogue (where we have a pair of sets instead of a single set). Joint work with Seoyoung Kim and Semin Yoo.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Pijush Pratim Sarmah (SFU) DTSTART:20240328T223000Z DTEND:20240328T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/114 DESCRIPTION:Title: Jacobians of Curves in Abelian Surfaces\nby Pijush Pratim Sarmah (S FU) 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 reducib ility theorem states that any abelian variety is isogenuous to a product o f simple abelian varieties. We are interested to know this decomposition f or Jacobians of smooth curves in abelian surfaces. Using Kani and Rosen's strikingly simple yet powerful theorem that relates subgroups of automorph ism groups with isogeny relations on Jacobians\, we will decompose Jacobia ns of certain curves coming from linear systems of polarizations on abelia n surfaces and comment on curve coverings.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Stanley Xiao (UNBC) DTSTART:20240404T223000Z DTEND:20240404T233000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/115 DESCRIPTION:Title: On Hilbert's Tenth Problem and a conjecture of Buchi\nby Stanley Xi ao (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 implications for Hilbert's Tenth Problem. In particular\, we show that if there is a tuple of five integer squares $(x_1^2\, x_2^2\, x_3^2\, x_4^2\, x_5^2)$ satisfy ing $x_{i+2}^2 - 2x_{i+1}^2 + x_i^2 = 2$ for $i = 1\,2\,3$\, then these mu st be consecutive squares. By an old result of J.R. Buchi\, this implies t hat there is no general algorithm which can decide whether an arbitrary sy stem of diagonal quadratic form equations admits a solution over the integ ers.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleonore Faber (University of Graz) DTSTART:20240222T233000Z DTEND:20240223T003000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/117 DESCRIPTION:Title: Friezes and resolutions of plane curve singularities\nby Eleonore F aber (University of Graz) as part of SFU NT-AG seminar\n\n\nAbstract\nConw ay-Coxeter friezes are arrays of positive integers satisfying a determinan tal condition\, the so-called diamond rule. Recently\, these combinatorial objects have been of considerable interest in representation theory\, sin ce they encode cluster combinatorics of type A.\n\nIn this talk I will dis cuss a new connection between Conway-Coxeter friezes and the combinatorics of a resolution of a complex curve singularity: via the beautiful relatio n between friezes and triangulations of polygons one can relate each friez e to the so-called lotus of a curve singularity\, which was introduced by Popescu-Pampu. This allows to interprete the entries in the frieze in term s of invariants of the curve singularity\, and on the other hand\, we can see cluster mutations in terms of the desingularization of the curve. This is joint work with Bernd Schober.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Pranabesh Das (XULA) DTSTART:20240704T173000Z DTEND:20240704T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/118 DESCRIPTION:Title: Sum of three consecutive fifth powers in an arithmetic progression\ nby Pranabesh Das (XULA) as part of SFU NT-AG seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/118/ END:VEVENT BEGIN:VEVENT SUMMARY:JM Landsberg (Texas A&M) DTSTART:20240815T223000Z DTEND:20240815T233000Z DTSTAMP:20260422T022949Z 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 classic al problem in linear algebra is to understand what are the linear subspace s of the\nspace of $m\\times n$ matrices such that no matrix in the space has full rank. This problem has connections\nto theoretical computer scien ce\, more precisely complexity theory\, and algebraic geometry. I will giv e\na history\, explain the connection to algebraic geometry (sheaves on pr ojective space satisfying\nvery special properties)\, and recent progress on the classification question. This is joint work\nwith Hang Huang.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Giesbrecht (Waterloo) DTSTART:20240725T173000Z DTEND:20240725T183000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/120 DESCRIPTION:Title: Functional Decomposition of Sparse Polynomials\nby Mark Giesbrecht (Waterloo) as part of SFU NT-AG seminar\n\nLecture held in AQ 5004.\n\nAbs tract\nWe consider the algorithmic problem of the functional decomposition 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\nwe ask h ow to quickly determine whether it can be be quickly written as a\ncomposi tion 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)\, Schin zel(1987)\, and Zannier(2008) have made\nmajor progress in showing that po lynomial roots and functional\ndecompositions of sparse polynomials\, rema in (fairly) sparse\, unlike\nfactorizations into irreducibels for example. \n\nComputationally\, we have had algorithms for functional decomposition of\ndense polynomials since Barton & Zippel (1976)\, though the first\npol ynomial-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 divide t he\ndegree.\n\nAlgorithms for polynomial decomposition that exploit sparsi ty have remained\nelusive until now. We demonstrate new algorithms which provide very fast\nsparsity-sensitive solutions to some of these problems. But important open\nalgorithmic problems remain\, including proving inde composibility\, and more\ngeneral sparse functional decomposition. And th ere is still considerable\nroom to tighten sparsity bounds in the underlyi ng mathematics and/or the\nimplied complexities.\n\nThis is ongoing work w ith Saiyue Liu (UBC) and Daniel S. Roche (USNA).\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Hendrik Süß (Jena) DTSTART:20240905T204500Z DTEND:20240905T214500Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/121 DESCRIPTION:Title: Local volumes of singularities and an algebraic Mahler conjecture\n by Hendrik Süß (Jena) as part of SFU NT-AG seminar\n\nLecture held in K9 509.\n\nAbstract\nIn my talk I will discuss the notion of local volume for singularities. For the special case of toric singularities this turns out to be closely related to the notion of Mahler volume in convex geometry. This opens a connection between algebraic geometry and unsolved questions around the Mahler volume. In particular\, I will discuss possible algebrai c interpretations of the well-known Mahler conjecture.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Shubhodip Mondal (UBC) DTSTART:20240912T203000Z DTEND:20240912T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/122 DESCRIPTION:Title: Dieudonné theory via cohomology of classifying stacks\nby Shubhodi p Mondal (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nA bstract\nClassically\, Dieudonné theory offers a linear algebraic classif ication of finite group schemes and p-divisible groups over a perfect fiel d of characteristic p>0. In this talk\, I will discuss generalizations of this story from the perspective of p-adic cohomology theory (such as cryst alline cohomology\, and the newly developed prismatic cohomology due to Bh att--Scholze) of classifying stacks.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Villagra Torcomian (SFU) DTSTART:20240919T203000Z DTEND:20240919T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/123 DESCRIPTION:Title: Perfect powers as sum of consecutive powers\nby Lucas Villagra Torc omian (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbst ract\nIn 1770 Euler observed that $3^3+4^3+5^3=6^3$ and asked if there was another perfect power that equals the sum of consecutive cubes. This capt ivated the attention of many important mathematicians\, such as Cunningham \, Catalan\, Genocchi and Lucas. In the last decade\, the more general equ ation $$x^k+(x+1)^k \\cdots (x+d)^k=y^n$$ began to be studied. \n\nIn this talk we will focus on this equation. We will see some known results and o ne of the most used tools to attack this kind of problems.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Netan Dogra (King's College London) DTSTART:20240926T203000Z DTEND:20240926T213000Z DTSTAMP:20260422T022949Z 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\nAbst ract\nLet $f(x)$ be a separable polynomial with rational number coefficien ts. In this talk I will review how the rational points of the hyperellipti c curve $y^2 = f(x)$ can sometimes be determined using the number field ob tained by adjoining a root of $f$\, via the Chabauty--Coleman method and t he theory of the $2$-Selmer group. I will then explain the limitations of this method\, and how to give a `nonabelian' generalisation. The punchline will be that\, if the Chabauty--Coleman method doesn't work\, we can some times determine the rational points using the field obtained by adjoining two roots of $f$.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/124/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART:20241114T213000Z DTEND:20241114T223000Z DTSTAMP:20260422T022949Z 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://researchseminars.org/talk/SFUQNTAG/125/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART:20250123T213000Z DTEND:20250123T223000Z DTSTAMP:20260422T022949Z 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://researchseminars.org/talk/SFUQNTAG/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Rahul Dalal (University of Vienna) DTSTART:20250227T203000Z DTEND:20250227T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/127 DESCRIPTION:Title: Automorphic Representations and Quantum Logic Gates (joint seminar with UBC)\nby Rahul Dalal (University of Vienna) as part of SFU NT-AG semi nar\n\n\nAbstract\nAny construction of a quantum computer requires finding a good set\nof universal quantum logic gates: abstractly\, a finite set o f matrices in\nU(2^n) such that short products of them can efficiently app roximate\narbitrary unitary transformations. The 2-qubit case n=2 is of pa rticular\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 en doscopic classification and higher-rank versions of the\nRamanujan bound-- -will play a crucial role in proving the necessary analytic\nestimate: spe cifically\, a weight-aspect variant of the density hypothesis\nfirst consi dered by Sarnak and Xue.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/127/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (PIMS Colloquium) DTSTART:20241017T203000Z DTEND:20241017T213000Z DTSTAMP:20260422T022949Z 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://researchseminars.org/talk/SFUQNTAG/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Ollivier (UBC) DTSTART:20241121T213000Z DTEND:20241121T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/130 DESCRIPTION:Title: Rigid dualizing complexes for affine Hecke algebras\nby Rachel Olli vier (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstr act\nGrothendieck's duality theory relies on the notion of a dualizing com plex. In the non-commutative setting such dualizing complexes were studied in the 90s beginning with work by Yekutieli. Since these complexes are no t unique (for example\, one can tensor them with any invertible object) Va n der Bergh subsequently introduced the notion of a rigid dualizing comple x.\n\nWe will discuss rigid dualizing complexes in the context of (generic ) affine Hecke algebras and see what sort of consequences one can draw.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Dijols (UBC) DTSTART:20241128T213000Z DTEND:20241128T223000Z DTSTAMP:20260422T022949Z 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 i n K9509.\n\nAbstract\nDistinguished representations are representations 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 Pla ncherel formula in a relative setting\, as well as in the Sakellaridis-Ven katesh conjectures for instance. I will explain how the Geometric Lemma al lows us to classify parabolically induced representations of the $p$-adic group $G_2$ distinguished by $SO_4$. In particular\, I will describe a new approach\, in progress\, where we use the structure of the p-adic octonio ns and their quaternionic subalgebras to describe the double coset space $ P\\backslash G_2/SO_4$\, where $P$ stands for the maximal parabolic subgro ups of $G_2$.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Tian Wang (Concordia) DTSTART:20250116T213000Z DTEND:20250116T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/133 DESCRIPTION:Title: Effective open image theorem for products of principally polarized abel ian varieties\nby Tian Wang (Concordia) as part of SFU NT-AG seminar\n \n\nAbstract\nLet $E/\\mathbb{Q}$ be an elliptic curve without complex mul tiplication. By Serre's open image theorem\, the mod $\\ell$ Galois repres entation $\\overline{\\rho}_{E\, \\ell}$ of $E$ is surjective for each pri me number $\\ell$ that is sufficiently large. Partially motivated by Serr e's uniformity question\, there has been research into an effective versio n of this result\, which aims to find an upper bound on the largest prime $\\ell$ such that $\\overline{\\rho}_{E\, \\ell}$ is nonsurjective. In thi s talk\, we consider an analogue of the problem for a product of principal ly polarized abelian varieties $A_1\, \\ldots\, A_n$ over $K$\, where the varieties are pairwise non-isogenous over $\\overline{K}$. We will presen t 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 Jacob Mayle .\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/133/ END:VEVENT BEGIN:VEVENT SUMMARY:No talk (OR Seminar) DTSTART:20241205T213000Z DTEND:20241205T223000Z DTSTAMP:20260422T022949Z 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://researchseminars.org/talk/SFUQNTAG/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Katrina Honigs (SFU) DTSTART:20250410T203000Z DTEND:20250410T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/135 DESCRIPTION:Title: McKay correspondence for reflection groups and derived categories\n by Katrina Honigs (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9 509.\n\nAbstract\nThe classical McKay correspondence shows that there 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 elegant c orrespondence\, but it's not at all obvious how to extend these ideas to o ther finite groups.\n\nKapranov and Vasserot\, and then\, later\, Bridgela nd\, King and Reid showed this correspondence can be recast and extended a s an equivalence of derived categories of coherent sheaves. When this fram ework is extended to finite subgroups of $\\mathrm{GL}(2\,\\mathbb{C})$ ge nerated by reflections\, the equivalence of categories becomes a semiortho gonal decomposition whose components are\, conjecturally\, in bijection wi th irreducible representations of $G$. This correspondence has been verifi ed in recent work of Potter and of Capellan for a particular embedding of the dihedral groups $D_n$ in $\\mathrm{GL}(2\,\\mathbb{C})$. I will discus s recent joint work verifying this decomposition in further cases.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Seda Albayrak (SFU) DTSTART:20250213T213000Z DTEND:20250213T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/136 DESCRIPTION:Title: Multivariate Generalization of Christol’s Theorem\nby Seda Albayr ak (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstrac t\nChristol's theorem (1979)\, which sets ground for many interactions bet ween theoretical computer science and number theory\, characterizes the co efficients of a formal power series over a finite field of positive charac teristic $p>0$ that satisfy an algebraic equation to be the sequences that can be generated by finite automata\, that is\, a finite-state machine ta kes the base-$p$ expansion of $n$ for each coefficient and gives the coeff icient 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 an d only if $f(n)$ is a $p$-automatic sequence. However\, this characterizat ion 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 algebra ic closure of $\\mathbb{F}_p (t)$ can be given in terms of $p$-quasi-autom atic generalized (Laurent) series. In fact\, the algebraic closure of $\\m athbb{F}_p (t)$ is precisely generalized Laurent series that are $p$-quasi -automatic. We will characterize elements in the algebraic closure of func tion fields over a field of positive characteristic via finite automata in the multivariate setting\, extending Kedlaya's results. In particular\, o ur aim is to give a description of the full algebraic closure for multivar iate fraction fields of positive characteristic.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Romina M. Arroyo (Universidad Nacional de Cordoba) DTSTART:20250109T213000Z DTEND:20250109T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/137 DESCRIPTION:Title: Complex structures on nilpotent almost abelian Lie algebras\nby Rom ina M. Arroyo (Universidad Nacional de Cordoba) as part of SFU NT-AG semin ar\n\nLecture held in K9509.\n\nAbstract\nThe question of which nilpotent Lie algebras admit complex structures is far from being understood. In rec ent decades\, progress has primarily focused on providing algebraic obstru ctions to the existence of such structures\, with classification results b eing limited to low-dimensional cases.\n\nThe aim of this talk is to intro duce the key concepts necessary to understand the problem\, including the definition of (nilpotent) Lie algebras\, the notion of a complex structure on them\, etc. Additionally\, I will present a recent classification resu lt for nilpotent almost abelian Lie algebras\, which was obtained through collaborative work with María Laura Barberis\, Verónica Díaz\, Yamile G odoy\, and María Isabel Hernández.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Gordon (UBC) DTSTART:20250306T213000Z DTEND:20250306T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/138 DESCRIPTION:Title: Improving integrability bounds for Harish-Chandra characters\nby Ju lia Gordon (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\ nAbstract\nIt is a well-known result of Harish-Chandra that most invariant distributions on real and p-adic reductive groups (e.g.\, Fourier transfo rms of orbital integrals\, and characters of representations) are represe nted by locally integrable functions on the group\, and the singularities of these functions are `smoothed' by the zeroes of the Weyl discriminant. In the recent joint work with Itay Glazer and Yotam Hendel\, we analyze the singularities of the inverse of the Weyl discriminant\, and from that\ , obtain an explicit improvement on the integrability exponent of the Four ier transforms of nilpotent orbital integrals\, and consequently\, of char acters (all these objects will be defined in the talk). I will discuss thi s improvement and some surprising applications\, e.g.\, to word maps.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (SFU) DTSTART:20250130T213000Z DTEND:20250130T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/139 DESCRIPTION:Title: Koszul-Tate Resolutions and Cotangent Cohomology for Monomial Ideals\nby Nathan Ilten (SFU) as part of SFU NT-AG seminar\n\nLecture held in K 9509.\n\nAbstract\nIntroduced by Tate in 1957\, a Koszul-Tate resolution a llows one to replace any algebra with a free differential graded algebra. This can be used to compute important invariants of the original algebra s uch as BRST cohomology or cotangent cohomology. I will report on a re-inte rpretation of recent work by Hancharuk\, Laurent-Gengoux\, and Strobl that constructs explicit Koszul-Tate resolutions. Using this\, I will then dis cuss some work in progress on higher cotangent cohomology for quotients of polynomial rings by monomial ideals. This is joint with Francesco Meazzin i and Andrea Petracci. No prior knowledge of Koszul-Tate resolutions or co tangent cohomology is assumed.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Jen Berg (Bucknell University) DTSTART:20250327T203000Z DTEND:20250327T213000Z DTSTAMP:20260422T022949Z 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 s eminar\n\n\nAbstract\nVarieties that fail to have rational points despite having local points for each prime are said to fail the Hasse principle. A systematic tool accounting for these failures uses the Brauer group to de fine an obstruction set known as the Brauer-Manin set. After fixing numeri cal invariants such as dimension\, it is natural to ask which birational c lasses of varieties fail the Hasse principle\, and moreover whether the Br auer 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 smooth sexti c curve) which are relatively simple surfaces in terms of geometric comple xity\, but have rich arithmetic. Via a purely geometric approach\, we cons truct a 3-torsion transcendental Brauer class on a degree 2 K3 surface whi ch obstructs the Hasse principle\, giving the first example of an obstruct ion of this type. This was joint work with Tony Varilly-Alvarado.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Greg Knapp (University of Calgary) DTSTART:20250403T203000Z DTEND:20250403T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/141 DESCRIPTION:Title: Upper bounds on polynomial root separation\nby Greg Knapp (Universi ty of Calgary) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nA bstract\nDistances between the roots of a fixed polynomial appear organica lly in many places in number theory. For any $f(x) \\in \\mathbb{Z}[x]$\, let $\\operatorname{sep}(f)$ denote the minimum distance between distinct roots of $f(x)$. Mahler initiated the study of separation by giving lowe r bounds on $\\operatorname{sep}(f)$ in terms of the degree and Mahler mea sure of $f(x)$\, and these bounds have been improved and generalized in re cent years. However\, there has been relatively little study concerning u pper bounds on $\\operatorname{sep}(f)$. In this talk\, I will describe r ecent work with Chi Hoi Yip in which we provide sharp upper bounds on $\\o peratorname{sep}(f)$ using techniques from the geometry of numbers.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Diana Mocanu (MPIM) DTSTART:20250313T163000Z DTEND:20250313T173000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/142 DESCRIPTION:Title: Generalized Fermat equations over totally real fields\nby Diana Moc anu (MPIM) as part of SFU NT-AG seminar\n\n\nAbstract\nWiles’ famous pro of of Fermat’s Last Theorem pioneered the so-called modular method\, in which modularity of elliptic curves is used to show that all integer solut ions of Fermat’s equation are trivial.\n\nIn this talk\, we briefly sket ch 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 equations. Th e main ingredients are modularity\, level lowering\, image of inertia comp arisons\, and S-unit equations.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Pries (Colorado State) DTSTART:20250320T203000Z DTEND:20250320T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/143 DESCRIPTION:Title: Supersingular curves in Hurwitz families\nby Rachel Pries (Colorado State) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract \nDespite extensive research\, it is not known whether Oort's conjecture a bout the existence of supersingular curves is true or false. In the first part of the talk\, I will describe supersingular curves and\ndiscuss the status of Oort's conjecture (both evidence for and counter-indications). In the second part of the talk\, I will explain: new existence results for supersingular curves of low genus (joint work with Booher)\; and mass for mulas for the number of supersingular curves in families (joint work with Cavalieri and Mantovan). This latter project generalizes the Eichler--Deu ring mass formula for supersingular elliptic curves. If time permits\, I will talk about basic reductions of genus four curves having an automorphi sm of order 5 (joint work with Li\, Mantovan\, Tang).\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/143/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine Leudière (University of Calgary) DTSTART:20250529T203000Z DTEND:20250529T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/144 DESCRIPTION:Title: A computation on Drinfeld modules\nby Antoine Leudière (University of Calgary) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbs tract\nThe development of algebraic geometry has shed light on deep simila rities between the classical number theory (characteristic zero\, number f ields)\, and its positive characteristic analogue (centered on curves and function fields). The latter turned out easier to work with: from a theore tical point of view\, some results are unconditional (e.g. Riemann hypothe sis for function fields)\; from a computational point of view\, a lot of e lementary procedures can be performed efficiently (e.g. polynomial factori zation\, as opposed to integer factorization).\n\nIn this talk\, we will m otivate Drinfeld modules: objects that play the role for function fields t hat elliptic curves play for number fields. We will give the example of th e computation of a group action from Class Field Theory whose classical an alogue is used in isogeny-based cryptography\, and rather slow to compute. \n LOCATION:https://researchseminars.org/talk/SFUQNTAG/144/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabien Pazuki (University of Copenhagen) DTSTART:20250918T203000Z DTEND:20250918T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/145 DESCRIPTION:Title: Isogeny volcanoes: an ordinary inverse problem.\nby Fabien Pazuki ( University of Copenhagen) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nIsogenies between elliptic curves have attracted a lot of attention\, and over finite fields the structures that they generate a re fascinating. For supersingular primes\, isogeny graphs are very connect ed. For ordinary primes\, isogeny graphs have a lot of connected component s and each of these components has the shape... of a volcano! An $\\ell$-v olcano graph\, to be precise\, with $\\ell$ a prime. We study the followin g inverse problem: if we now start by considering a graph that has an $\\e ll$-volcano shape (we give a precise definition\, of course)\, how likely is it that this abstract volcano can be realized as a connected component of an isogeny graph?\n\nWe prove that any abstract $\\ell$-volcano graph c an be realized as a connected component of the $\\ell$-isogeny graph of an ordinary elliptic curve defined over $\\mathbb{F}_p$\, where $\\ell$ and $p$ are two different primes. If time permits\, we will touch upon some ne w applications and new challenges. This is joint work with Henry Bambury a nd Francesco Campagna.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Tarnu (Simon Fraser University) DTSTART:20251016T203000Z DTEND:20251016T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/146 DESCRIPTION:Title: Limiting behavior of Rudin-Shapiro sequence autocorrelations\nby Da niel Tarnu (Simon Fraser University) as part of SFU NT-AG seminar\n\nLectu re held in K9509.\n\nAbstract\nThe Rudin-Shapiro polynomials $p_{m}$ were first studied by Rudin\, Shapiro\, and Golay independently nearly 80 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 from ric h structure and is of special interest as a subset of Littlewood polynomia ls (i.e.\, polynomials with coefficients in $\\{ -1\, 1 \\}$)\, in part du e to their having small $L^{4}$ norm\, which is desirable and almost alway s unsatisfied by Littlewood polynomials in general. In application\, uses are found for the Rudin-Shapiro polynomials in varied contexts such as rad io 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 called t he $m$-th Rudin-Shapiro sequence. We denote by $C_{m}(k)$ the aperiodic au tocorrelation 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 understood that $a_{j} = 0$ for $j \\notin [0\, 2^{m}-1]$. These autocorrelations have be en studied extensively. It is often difficult to determine or approximate $C_{m}(k)$ 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 give the precise orders of $\\sum_{0 < k \\leq x} (C_{m}(k))^{2} $ and $\\max_{0 < k \\leq x} |C_{m}(k)|$\, 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 = \\frac{2}{3} $\, supporting our conjecture that the maximum value of $|C_{m}(k)|$ occur s uniquely at some $k_{m}^{\\ast}$ with $\\lim_{m \\to \\infty} \\frac{k_{ m}^{\\ast}}{2^{m}} = \\frac{2}{3}$. This is joint work with Stephen Choi.\ n LOCATION:https://researchseminars.org/talk/SFUQNTAG/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Shabnam Akhtari (Penn State) DTSTART:20250925T203000Z DTEND:20250925T213000Z DTSTAMP:20260422T022949Z 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\nAbstract\ nLet $K$ be an algebraic number field. The Primitive Element Theorem impli es that the number field $K$ can be generated over the field of rational n umbers by a single element of $K$. We call such an element a generator of $K$. A simple and natural question is “What is the smallest generator of a given number field?” (and how to find it!) In order to express this q uestion more precisely\, we will introduce some height functions. Then we will discuss some open problems and some recent progress in this area\, in cluding a joint project with Jeff Vaaler and Martin Widmer.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Josiah Foster (University of Oregon) DTSTART:20251023T203000Z DTEND:20251023T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/148 DESCRIPTION:Title: The Lefschetz standard conjectures for Kummer-type hyper-Kaehler variet ies\nby Josiah Foster (University of Oregon) as part of SFU NT-AG semi nar\n\nLecture held in K9509.\n\nAbstract\nFor a complex projective variet y\, the Lefschetz standard conjectures predict the existence of algebraic self-correspondences that are inverse to the hard Lefschetz isomorphisms. They have broad implications for Hodge theory and the theory of motives. We describe recent progress on the Lefschetz standard conjectures for irr educible holomorphic symplectic (compact hyper-Kaehler) manifolds of gener alized Kummer deformation type.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Berget (Western Washington University) DTSTART:20251106T213000Z DTEND:20251106T223000Z DTSTAMP:20260422T022949Z 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 seminar\n\nLe cture held in K9509.\n\nAbstract\nIn his 2005 PhD thesis on tropical linea r spaces\, Speyer conjectured an upper bound on the number of interior fac es in a matroid base polytope subdivision of a hypersimplex. This conjectu re can be reduced to determining the sign of the Euler characteristic 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 matroids\ , and extend this to a statement about pairs of matroids on the same groun d set. In this talk\, I will provide an overview of our strategy and zoom in on how we extend geometric results for realizable pairs of matroids to all pairs.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter McDonald (SFU) DTSTART:20251002T203000Z DTEND:20251002T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/150 DESCRIPTION:Title: The Briançon--Skoda property for singular rings via closure operations \nby Peter McDonald (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nIn 1974\, Briançon and Skoda answered a question of Mather\, showing that for $I=(f_1\,\\dots\,f_n)$ an ideal of the coordi nate ring at a smooth point on a complex algebraic variety\, there is a co ntainment $\\overline{I^{n+k-1}}\\subseteq I^k$ for all $k\\geq1$. To the dismay of algebraists\, this was achieved using analytic techniques\, lead ing Lipman and Sathaye in 1981 to supply an algebraic proof to give a simi lar bound for ideals in regular rings in all characteristics. Generally\, this containment fails for singular rings\, though work of many people hav e given results for singular rings in various settings. In this talk\, I'l l discuss recent joint work with Neil Epstein\, Rebecca RG\, and Karl Schw ede where we give a characteristic-free proof of the desired containment f or a large class of singular rings\, implying many of the previously-known Brian\\c{c}on--Skoda type results.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/150/ END:VEVENT BEGIN:VEVENT SUMMARY:Allechar Serrano López (Montana State University) DTSTART:20251009T203000Z DTEND:20251009T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/151 DESCRIPTION:Title: Counting number fields\nby Allechar Serrano López (Montana State U niversity) as part of SFU NT-AG seminar\n\n\nAbstract\nA guiding question 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 normal clo sure has Galois group $G$ grow as their discriminants tend to infinity? In this talk\, I will give an overview of the history and development of num ber field asymptotics\, and we will obtain a count for dihedral quartic ex tensions over a fixed number field.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/151/ END:VEVENT BEGIN:VEVENT SUMMARY:Alicia Lamarche (Yau Mathematical Sciences Center) DTSTART:20251127T213000Z DTEND:20251127T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/152 DESCRIPTION:Title: Wonderful Compactifications for the Algebraic Geometer\nby Alicia L amarche (Yau Mathematical Sciences Center) as part of SFU NT-AG seminar\n\ nLecture held in K9509.\n\nAbstract\nGiven a complex Lie group G of adjoin t 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 diagrams and corresponding root systems\, from which one can construct a toric variety X(G). In this talk\, we will discuss ongoing work with Aaron Bertram that aims to succinctly describe the structure of Y(G) and X(G) in terms of bi rational geometry.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/152/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Frei (Rice University) DTSTART:20251030T203000Z DTEND:20251030T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/153 DESCRIPTION:Title: Cubic fourfolds with birational Fano varieties of lines\nby Sarah F rei (Rice University) as part of SFU NT-AG seminar\n\nLecture held in K950 9.\n\nAbstract\nCubic fourfolds have been classically studied up to birati onal equivalence\, with a view toward the rationality problem. The Fano va riety of lines F(X) on a cubic fourfold X is a hyperkähler manifold\, and the rationality of X is conjecturally captured by the geometry of F(X). I n joint work with C. Brooke and L. Marquand\, building on our previous wor k with X. Qin\, we study pairs of conjecturally irrational cubic fourfolds with birational Fano varieties of lines. We provide new examples of pairs of cubic fourfolds with equivalent Kuznetsov components. Moreover\, we sh ow that the cubic fourfolds themselves are birational.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Staal (University of the Fraser Valley) DTSTART:20251120T213000Z DTEND:20251120T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/154 DESCRIPTION:Title: Recent Examples of Elementary Components of Hilbert Schemes of Points\nby Andrew Staal (University of the Fraser Valley) as part of SFU 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 describe some recent examples of elementary components of Hilbert schemes of points. O ne infinite family of these answers a question posed by Iarrobino in the 8 0's: does there exist an irreducible component of the (local) punctual Hil bert scheme $\\operatorname{Hilb}^d(\\mathscr{O}_{\\mathbb{A}^n\,p})$ of d imension less than $(n-1)(d-1)$? A different family of elementary compone nts arises from the Galois closure operation introduced by Bhargava--Satri ano. In both situations\, secondary families of elementary components als o arise\, providing further new examples of elementary components of Hilbe rt schemes of points.\n\nThis is joint work with Matt Satriano (U Waterloo ).\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Joshua Turner (UBC) DTSTART:20251113T213000Z DTEND:20251113T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/155 DESCRIPTION:Title: Haiman ideals\, link homology\, and affine Springer fibers\nby Josh ua Turner (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\n Abstract\nWe will discuss a class of ideals in a polynomial ring studied b y Mark Haiman in his work on the Hilbert scheme of points and discuss how they are related to homology of affine Springer fibers\, Khovanov-Rozansky homology of links\, and to the ORS conjecture. We will also discuss how t o compute KR-homology using combinatorial braid recursions developed by El ias and Hogancamp.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/155/ END:VEVENT BEGIN:VEVENT SUMMARY:Felix Thimm (UBC) DTSTART:20260115T213000Z DTEND:20260115T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/156 DESCRIPTION:Title: Wall-Crossing and the DT/PT3 Descendant Correspondence\nby Felix Th imm (UBC) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstra ct\nDonaldson–Thomas and Pandharipande–Thomas invariants are two ways of counting curves in Calabi-Yau 3-folds\, related by a change of stabilit y conditions. Wall-crossing is a technique that allows us to compare enume rative invariants under such a change in stability condition. It has emerg ed as a powerful tool for computations and in the study of properties of g enerating series of various types of enumerative invariants. I will presen t joint work with N. Kuhn and H. Liu on how to use (virtual) localization to wall-cross more general invariants with descendant insertions. In the p rocess I will explain how Juanolou's trick from classical algebraic geomet ry comes in as a useful and central ingredient.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/156/ END:VEVENT BEGIN:VEVENT SUMMARY:Seda Albayrak (SFU) DTSTART:20260129T213000Z DTEND:20260129T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/157 DESCRIPTION:Title: Quantitative estimates on the size of an intersection of sparse automat ic sets\nby Seda Albayrak (SFU) as part of SFU NT-AG seminar\n\nLectur e held in K9509.\n\nAbstract\nIn this talk\, I will talk about use of auto mata theory in answering problems in number theory. In 1844\, Catalan conj ectured 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 intersection. In fact\, we can answer such question in more generality\, that is\, inst ead of $2$ and $3$\, we can show this for $k$ and $\\ell$ that are multipl icatively independent (meaning if $k^a=\\ell^b$\, then $a=b=0$). In automa ta-theoretic terms\, these sets described above are sparse $2$-automatic a nd sparse $3$-automatic sets\, respectively. In fact\, a sparse $k$-automa tic set can be more complicated than having elements that are of the form $k^n$ or $k^n+1$\, and hence\, we are answering an even more general quest ion. Moreover\, we also prove our result in a multidimensional setting in line with the existing results in the theory of formal languages and finit e automata. We show that the intersection of a sparse $k$-automatic subset of $\\mathbb{N}^d$ and a sparse $\\ell$-automatic subset of $\\mathbb{N}^ d$ is finite and we give effectively computable upper bounds on the size o f the intersection in terms of data from the automata that accept these se ts. We will also see how all of this is related to a conjecture of Erdös. \n LOCATION:https://researchseminars.org/talk/SFUQNTAG/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Villagra Torcomian (SFU) DTSTART:20260226T213000Z DTEND:20260226T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/158 DESCRIPTION:Title: The role of hyperelliptic curves in the modular method\nby Lucas Vi llagra Torcomian (SFU) as part of SFU NT-AG seminar\n\nLecture held in K95 09.\n\nAbstract\nAfter a brief review of the modular method\, in this talk we will explain how hyperelliptic curves have emerged as an important too l in recent years to approach generalized Fermat equations.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/158/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Bruin (SFU) DTSTART:20260205T213000Z DTEND:20260205T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/159 DESCRIPTION:Title: 2-isogenies on Jacobians of genus 3 curves\nby Nils Bruin (SFU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nWe consid er isogenies on Jacobians J of genus 3 curves with a kernel that is a maxi mal isotropic subgroup of the 2-torsion J[2] and confront a phenomenon tha t is new in genus 3: for genus 1 and 2 the codomain is generally again a J acobian of a curve and we have\nan explicit construction of that curve. In the genus 3 case we only obtain that the codomain is a quadratic twist of a Jacobian.\n\nWe use a construction by Donagi-Livne\, refined by Lehavi- Ritzenthaler that constructs the curve whose Jacobian is the codomain up t o quadratic twist. We refine the construction further to explicitly determ ine this quadratic twist and use it to compute many examples. The construc tion requires the specification of a flag on the isogeny kernel and constr ucts the codomain in steps\, in terms of various Prym varieties.\n\nThis i s joint work with Damara Gagnier.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu Shen (Michigan State University) DTSTART:20260212T213000Z DTEND:20260212T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/160 DESCRIPTION:Title: Picard group action on the category of twisted sheaves\nby Yu Shen (Michigan State University) as part of SFU NT-AG seminar\n\nLecture held i n K9509.\n\nAbstract\nIn this talk\, I will discuss the category of twiste d sheaves on a scheme $X$. Let $\\mathcal{M}$ be a quasi-coherent sheaf 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 $D^{b}(X\, \\alph a)$ is faithful for any Noetherian scheme $X$. We also show that taking Br auer twists of varieties does not yield new Calabi--Yau categories. This i s joint work with Ting Gong and Yeqin Liu.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/160/ END:VEVENT BEGIN:VEVENT SUMMARY:Janet Page (North Dakota State University) DTSTART:20260402T203000Z DTEND:20260402T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/161 DESCRIPTION:Title: Smooth Surfaces with Maximally Many Lines\nby Janet Page (North Dak ota State University) as part of SFU NT-AG seminar\n\nLecture held in K950 9.\n\nAbstract\nHow many lines can lie on a smooth surface of degree d? T his classical question in algebraic geometry has been studied since at lea st the mid 1800s\, when Clebsch gave an upper bound of d(11d-24) for the n umber of lines on a smooth surface of degree d over the complex numbers. 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. Ho wever\, over a field of characteristic p < d\, there are smooth projective 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 smoot h surface of degree d which holds over any field. In addition\, we’ll f ully classify those surfaces which attain this upper bound and talk about some of their other surprising properties. This talk is based on joint wo rk with Tim Ryan and Karen Smith.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/161/ END:VEVENT BEGIN:VEVENT SUMMARY:Yixin Chen DTSTART:20260409T203000Z DTEND:20260409T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/162 DESCRIPTION:Title: Transcendental Brauer-Manin Obstruction for Hyperelliptic Surfaces\ nby Yixin Chen as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nA bstract\nThe Brauer–Manin obstruction provides a powerful framework for explaining failures of the Hasse principle for rational points on algebrai c varieties. While many known examples arise from the algebraic part of th e Brauer group\, comparatively few explicit constructions exhibit genuinel y transcendental obstructions.\n\nIn this talk\, we will present a concret e example of a transcendental Brauer–Manin obstruction to the existence of rational points on a $K3$ surface. We will use a hyperelliptic fibered surface that is birational to this $K3$ surface to help construct the Brau er-Manin obstruction.\n\nThis example illustrates how fibration techniques can be used to produce and control transcendental elements in the Brauer group.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Wills (University of Virginia) DTSTART:20260319T203000Z DTEND:20260319T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/163 DESCRIPTION:Title: Local-to-global principles for zero-cycles\nby Michael Wills (Unive rsity of Virginia) as part of SFU NT-AG seminar\n\n\nAbstract\nIn arithmet ic geometry\, local-to-global principles capture the ways in which one app roaches difficult "global" questions over number fields by studying their "local" analogues over $p$-adic fields. These principles often fail for qu estions about the rational points of an algebraic variety. However\, a con jecture of Colliot-Th$\\text{\\'e}$l$\\text{\\`e}$ne states that by genera lizing the question to zero-cycles one might recover a successful local-to -global principle. In this talk\, we present some recent evidence for this conjecture for products of elliptic curves with complex multiplication.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/163/ END:VEVENT BEGIN:VEVENT SUMMARY:Graham McDonald (SFU) DTSTART:20260305T213000Z DTEND:20260305T223000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/164 DESCRIPTION:Title: Curves in linear systems on abelian surfaces\nby Graham McDonald (S FU) as part of SFU NT-AG seminar\n\nLecture held in K9509.\n\nAbstract\nLe t $A$ be an abelian surface. We investigate curves in a linear system on t he dual abelian surface $\\hat{A}$. There is an isomorphism of moduli spac es due to Yoshioka between the space $K_3(A)$ parametrizing 0-dimensional length-4 subschemes on $A$ that sum to the identity in the group law\, and the space $K_{\\hat{A}}(0\,\\hat{\\ell}\,-1)$ parametrizing certain rank 1 torsion free sheaves supported on curves in a linear system on $\\hat{A} $. Leveraging this isomorphism together with quadratic forms associated to symmetric line bundles on $A$\, we develop a computational method that al lows us to characterize the singularities of the curves that correspond to a finite distinguished subset of $K_3(A)$. In this talk we will describe these methods and compute an example of a curve with two nodal singulariti es.\n\nThis is joint work with Katrina Honigs and Peter McDonald.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/164/ END:VEVENT BEGIN:VEVENT SUMMARY:Negarin Mohammadi (Simon Fraser University) DTSTART:20260312T203000Z DTEND:20260312T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/165 DESCRIPTION:Title: Arithmetic Prym Constructions and (1\,2)-Polarized Abelian Surfaces \nby Negarin Mohammadi (Simon Fraser University) as part of SFU NT-AG semi nar\n\nLecture held in K9509.\n\nAbstract\nWe construct explicit examples of abelian surfaces whose 2-torsion Galois representations are not self-du al. Such surfaces are necessarily not principally polarized. We consider a belian surfaces with a polarization of type (1\,2) instead. Our main 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. We use a Galois-theoretic construction of Donagi and Pantazis to express the dual also as a Prym variety of the same type. The 2-torsion $P[2]$ naturally em beds in $J_C[2]$\, where the classical geometry of plane quartics\, bitang ents\, and theta characteristics gives concrete access to the Galois actio n. \n\nConversely\, we prove that every (1\,2)-polarized abelian surface o ver a base field of characteristic other than 2 can be realized as a biell iptic Prym. Barth already proved this over algebraically closed base field s\, and we extend it to arbitrary fields. This is achieved by factoring th e polarization $\\rho : A \\to A^\\vee$ through a principally polarized su rface $J$. We then show that an appropriate plane section of the Kummer su rface of $J$ yields an elliptic curve $E$ with a genus 3 double cover $C \ \to E$ such that $A^\\vee = \\mathrm{Prym}(C \\to E)$. A careful Galois d escent argument then allows us to deduce the general case.\n\nThis is join t work with Nils Bruin and Katrina Honigs.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/165/ END:VEVENT BEGIN:VEVENT SUMMARY:No seminar (PIMS Colloquium) DTSTART:20260326T203000Z DTEND:20260326T213000Z DTSTAMP:20260422T022949Z 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://researchseminars.org/talk/SFUQNTAG/166/ END:VEVENT BEGIN:VEVENT SUMMARY:Bianca Viray (University of Washington) DTSTART:20260513T180000Z DTEND:20260513T190000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/167 DESCRIPTION:Title: Unlikely ramification in residue fields of points on curves\nby Bia nca Viray (University of Washington) as part of SFU NT-AG seminar\n\nLectu re held in K9509.\n\nAbstract\nAn accepted truism in arithmetic geometry i s that curves of genus at least 2 have more complicated arithmetic than cu rves of genus 0 or 1. One way this is made precise is by Faltings's Theore m: any curve of genus at least 2 has only finitely many points over any nu mber field. Another possibility for making this precise is to show that th ere are many number fields that cannot appear as the residue field of poin ts on a fixed curve of genus at least 2. In this talk\, we report on resul ts in this direction\, joint with Isabel Vogt.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/167/ END:VEVENT BEGIN:VEVENT SUMMARY:Ram Murty (Queen's University) DTSTART:20260501T203000Z DTEND:20260501T213000Z DTSTAMP:20260422T022949Z UID:SFUQNTAG/168 DESCRIPTION:Title: Multivariable arithmetical functions and their associated Dirichlet ser ies\nby Ram Murty (Queen's University) as part of SFU NT-AG seminar\n\ nLecture held in K9509.\n\nAbstract\nWe will discuss the emerging theory o f multivariable arithmetical functions and their\nassociated Dirichlet ser ies to be viewed as complex analytic functions of several variables. We\nw ill also present several applications of the theory to some current open p roblems of classical\nanalytic number theory.\n\nRam Murty will also give a talk at 3:00 PM\, Monday\, May 11\, at K9509\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/168/ END:VEVENT END:VCALENDAR