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;VALUE=DATE-TIME:20200521T170000Z DTEND;VALUE=DATE-TIME:20200521T180000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20200528T223000Z DTEND;VALUE=DATE-TIME:20200528T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20200604T223000Z DTEND;VALUE=DATE-TIME:20200604T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20200611T223000Z DTEND;VALUE=DATE-TIME:20200611T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20200625T223000Z DTEND;VALUE=DATE-TIME:20200625T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20200702T223000Z DTEND;VALUE=DATE-TIME:20200702T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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 ofAfter 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;VALUE=DATE-TIME:20200709T223000Z DTEND;VALUE=DATE-TIME:20200709T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20200716T223000Z DTEND;VALUE=DATE-TIME:20200716T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20200723T223000Z DTEND;VALUE=DATE-TIME:20200723T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20201029T163000Z DTEND;VALUE=DATE-TIME:20201029T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20201105T173000Z DTEND;VALUE=DATE-TIME:20201105T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20201112T173000Z DTEND;VALUE=DATE-TIME:20201112T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20201126T173000Z DTEND;VALUE=DATE-TIME:20201126T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20201119T173000Z DTEND;VALUE=DATE-TIME:20201119T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20201203T173000Z DTEND;VALUE=DATE-TIME:20201203T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20201210T173000Z DTEND;VALUE=DATE-TIME:20201210T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210121T173000Z DTEND;VALUE=DATE-TIME:20210121T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210128T173000Z DTEND;VALUE=DATE-TIME:20210128T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210225T173000Z DTEND;VALUE=DATE-TIME:20210225T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210204T173000Z DTEND;VALUE=DATE-TIME:20210204T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210415T163000Z DTEND;VALUE=DATE-TIME:20210415T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210408T163000Z DTEND;VALUE=DATE-TIME:20210408T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210304T173000Z DTEND;VALUE=DATE-TIME:20210304T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210318T163000Z DTEND;VALUE=DATE-TIME:20210318T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210325T163000Z DTEND;VALUE=DATE-TIME:20210325T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210311T173000Z DTEND;VALUE=DATE-TIME:20210311T183000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210401T163000Z DTEND;VALUE=DATE-TIME:20210401T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210527T163000Z DTEND;VALUE=DATE-TIME:20210527T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210610T163000Z DTEND;VALUE=DATE-TIME:20210610T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210708T163000Z DTEND;VALUE=DATE-TIME:20210708T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210624T163000Z DTEND;VALUE=DATE-TIME:20210624T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210715T163000Z DTEND;VALUE=DATE-TIME:20210715T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210617T163000Z DTEND;VALUE=DATE-TIME:20210617T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210722T163000Z DTEND;VALUE=DATE-TIME:20210722T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210729T163000Z DTEND;VALUE=DATE-TIME:20210729T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210812T163000Z DTEND;VALUE=DATE-TIME:20210812T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210916T163000Z DTEND;VALUE=DATE-TIME:20210916T173000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20211028T223000Z DTEND;VALUE=DATE-TIME:20211028T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20211118T233000Z DTEND;VALUE=DATE-TIME:20211119T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20211104T223000Z DTEND;VALUE=DATE-TIME:20211104T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20211021T223000Z DTEND;VALUE=DATE-TIME:20211021T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20211209T233000Z DTEND;VALUE=DATE-TIME:20211210T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20211202T233000Z DTEND;VALUE=DATE-TIME:20211203T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20210923T223000Z DTEND;VALUE=DATE-TIME:20210923T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20211007T223000Z DTEND;VALUE=DATE-TIME:20211007T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20211014T223000Z DTEND;VALUE=DATE-TIME:20211014T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220113T233000Z DTEND;VALUE=DATE-TIME:20220114T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220203T233000Z DTEND;VALUE=DATE-TIME:20220204T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220210T233000Z DTEND;VALUE=DATE-TIME:20220211T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220217T233000Z DTEND;VALUE=DATE-TIME:20220218T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220303T233000Z DTEND;VALUE=DATE-TIME:20220304T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220324T223000Z DTEND;VALUE=DATE-TIME:20220324T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220317T223000Z DTEND;VALUE=DATE-TIME:20220317T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220331T223000Z DTEND;VALUE=DATE-TIME:20220331T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220407T223000Z DTEND;VALUE=DATE-TIME:20220407T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220414T223000Z DTEND;VALUE=DATE-TIME:20220414T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220915T223000Z DTEND;VALUE=DATE-TIME:20220915T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220922T223000Z DTEND;VALUE=DATE-TIME:20220922T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20220929T223000Z DTEND;VALUE=DATE-TIME:20220929T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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\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;VALUE=DATE-TIME:20240307T233000Z DTEND;VALUE=DATE-TIME:20240308T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20240314T223000Z DTEND;VALUE=DATE-TIME:20240314T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20240321T223000Z DTEND;VALUE=DATE-TIME:20240321T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20240328T223000Z DTEND;VALUE=DATE-TIME:20240328T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20240404T223000Z DTEND;VALUE=DATE-TIME:20240404T233000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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;VALUE=DATE-TIME:20240222T233000Z DTEND;VALUE=DATE-TIME:20240223T003000Z DTSTAMP;VALUE=DATE-TIME:20240423T115424Z 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 END:VCALENDAR