Joint work with Markus Kirschmer\, Fabien Narbonne and Da mien Robert

\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:20210419T101258Z UID:SFUQNTAG/3 DESCRIPTION:Title: Regulators of number fields and abelian varieties\nby Fabien Pazuki ( Copenhagen) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nIn the general study of regulators\, we present three inequalities. We first bou nd from below the regulators of number fields\, following previous works o f Silverman and Friedman. We then bound from below the regulators of Morde ll-Weil groups of abelian varieties defined over a number field\, assuming a conjecture of Lang and Silverman. Finally we explain how to prove an un conditional statement for elliptic curves of rank at least 4. This third i nequality is joint work with Pascal Autissier and Marc Hindry. We give som e corollaries about the Northcott property and about a counting problem fo r rational points 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:20210419T101258Z UID:SFUQNTAG/4 DESCRIPTION:Title: Fano schemes for complete intersections in toric varieties\nby Nathan Ilten (SFU) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nThe s tudy of the set of lines contained in a fixed hypersurface is classical: C ayley and Salmon showed in 1849 that a smooth cubic surface contains 27 li nes\, and Schubert showed in 1879 that a generic quintic threefold contain s 2875 lines. More generally\, the set of k-dimensional linear spaces cont ained in a fixed projective variety X itself is called the k-th Fano schem e of X. These Fano schemes have been studied extensively when X is a gener al hypersurface or complete intersection in projective space.\n\nIn thi s talk\, I will report on work with Tyler Kelly in which we study Fano sch emes for hypersurfaces and complete intersections in projective toric vari eties. In particular\, I'll give criteria for the Fano schemes of generic complete intersections 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 d egree (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:20210419T101258Z UID:SFUQNTAG/5 DESCRIPTION:Title: The Dubrovin threefold of an algebraic curve\nby Türkü Özlüm Çel ik (Leipzig University) as part of SFU Quarantined NT-AG Seminar\n\n\nAbst ract\nThe solutions to the Kadomtsev-Petviashvili equation that arise from a fixed\ncomplex algebraic curve are parametrized by a threefold in a wei ghted projective space\,\nwhich we name after Boris Dubrovin. Current meth ods from nonlinear algebra are applied\nto study parametrizations and defi ning ideals of Dubrovin threefolds. We highlight the\ndichotomy between tr anscendental 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:20210419T101258Z UID:SFUQNTAG/6 DESCRIPTION:Title: Boij-Söderberg Theory for Grassmannians\nby Jake Levinson (Universit y of Washington) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nT he Betti table of a graded module over a polynomial ring encodes much of i ts structure and that of the corresponding sheaf on projective space. In g eneral\, it is hard to tell which integer matrices can arise as Betti tabl es. An easier problem is to describe such tables up to positive scalar mul tiple: 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 w ith Nicolas Ford and Steven Sam\, to the setting of GL-equivariant modules over coordinate rings of matrices. Here\, the dual theory (in geometry) c oncerns sheaf cohomology on Grassmannians. One theorem of interest is an e quivariant analog of the Boij-Söderberg pairing between Betti tables and cohomology tables. This is a bilinear pairing of cones\, with output in th e cone coming from the "base case" of square matrices\, which we also full y characterize.

\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:20210419T101258Z UID:SFUQNTAG/7 DESCRIPTION:Title: pNumerical Linear Algebra\nby Avinash Kulkarni (Darmouth) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nIn this talk\, I will present new algorithms\, based on ideas from numerical analysis\, for efficiently computing the generalized eigenspaces of a square matrix with finite prec ision p-adic entries. I will then discuss how these eigenvector methods ca n be used to compute the (approximate) solutions to a zero-dimensional pol ynomial system.\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:20210419T101258Z UID:SFUQNTAG/8 DESCRIPTION:Title: Moduli spaces of Mumford curves over Z\nby Daniele Turchetti (Dalhous ie) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nSchottky unifo rmization is the description of an analytic curve as the quotient of an op en dense subset of the projective line by the action of a Schottky group.\ nAll complex curves admit this uniformization\, as well as some $p$-adic c urves\, called Mumford curves.\nIn this talk\, I present a construction ofAfter introducing P oineau's theory from scratch\, I will describe universal Mumford curves an d explain how these can be used as a framework to study the Tate curve and to give higher genus generalizations of it. This is based on joint work w ith 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:20210419T101258Z UID:SFUQNTAG/9 DESCRIPTION:Title: Rational surfaces and locally recoverable codes\nby Anthony Várilly- Alvarado (Rice University) as part of SFU Quarantined NT-AG Seminar\n\n\nA bstract\nMotivated by large-scale storage problems around data loss\, a bu dding branch of coding theory has surfaced in the last decade or so\, cent ered around locally recoverable codes. These codes have the property that individual symbols in a codeword are functions of other symbols in the sam e word. If a symbol is lost (as opposed to corrupted)\, it can be recomput ed\, and hence a code word can be repaired. Algebraic geometry has a role to play in the design of codes with locality properties. In this talk I wi ll explain how to use algebraic surfaces birational to the projective plan e to both reinterpret 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 a nd Felipe Voloch.\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:20210419T101258Z UID:SFUQNTAG/10 DESCRIPTION:Title: Isolated points on modular curves\nby Bianca Viray (University of Wa shington) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nFaltings 's theorem on rational points on subvarieties of\nabelian varieties can be used to show that all but finitely many\nalgebraic points on a curve aris e in families parametrized by $\\mathbb{P}^1$ or\npositive rank abelian va rieties\; we call these finitely many\nexceptions isolated points. We stu dy how isolated points behave under\nmorphisms and then specialize to the case of modular curves. We show\nthat isolated points on $X_1(n)$ push do wn to isolated points on a\nmodular curve whose level is bounded by a cons tant that depends 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:20210419T101258Z 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 Quaranti ned NT-AG Seminar\n\n\nAbstract\nFor a curve C over a global field K it ha s been conjectured that the Brauer-Manin obstruction explains all failures of the Hasse principle. I will discuss results toward this conjecture in the case of constant curves over a global function field\, i.e. where C an d D are curves over a finite field and we consider C over the function fie ld of D. This 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:20210419T101258Z 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 Quarantined NT-AG Seminar\ n\n\nAbstract\nDel Pezzo surfaces are classified by their degree d\, which is an integer between $1$ and $9$ (for $d ≥ 3$\, these are the smooth s urfaces of degree $d$ in $\\mathbb{P}^d$). For del Pezzo surfaces of degre e at least $2$ over a field $k$\, we know that the set of $k$-rational poi nts is Zariski dense provided that the surface has one $k$-rational point to start with (that lies outside a specific subset of the surface for degr ee $2$). However\, for del Pezzo surfaces of degree $1$ over a field k\, e ven though we know that they always contain at least one $k$-rational poin t\, we do not know if the set of $k$-rational points is Zariski dense in g eneral. I will talk about a result that is joint work with Julie Desjardin s\, in which we give necessary and sufficient conditions for the set of $k $-rational points on a specific family of del Pezzo surfaces of degree $1$ to be Zariski dense\, where k is a number field. I will compare this to p revious results.\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:20210419T101258Z UID:SFUQNTAG/13 DESCRIPTION:Title: Explicit Vologodsky Integration for Hyperelliptic Curves\nby Enis Ka ya (University of Groningen) as part of SFU Quarantined NT-AG Seminar\n\n\ nAbstract\nLet $X$ be a curve over a $p$-adic field with semi-stable reduc tion and let $\\omega$ be a \nmeromorphic $1$-form on $X$. There are two n otions of p-adic integration one may associate \nto this data: the Berkovi ch–Coleman integral which can be performed locally\; and the \nVologodsk y integral with desirable number-theoretic properties. In this talk\, we p resent a \ntheorem comparing the two\, and describe an algorithm for compu ting Vologodsky integrals \nin the case that $X$ is a hyperelliptic curve. We also illustrate our algorithm with a numerical \nexample computed in S age. This talk 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:20210419T101258Z 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 Quarantined 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 ha s CM by O we need to construct class polynomials\, and for doing this we n eed to control the primes in the discriminant of the curves and their expo nents. In previous works I studied the so-called "embedding problem" in or der to bound the primes of bad reduction. In the present one we give an al gorithm to explicitly compute them and we bound the exponent of those prim es in the discriminant for the hyperelliptic case. Several examples will b e given.\n\n(joint work with S. Ionica\, P. Kilicer\, K. Lauter\, A. Manza teanu 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:20210419T101258Z UID:SFUQNTAG/15 DESCRIPTION:Title: Separating periods of quartic surfaces\nby Emre Sertöz (Max Planck Institute for Mathematics) as part of SFU Quarantined NT-AG Seminar\n\n\nA bstract\nKontsevich--Zagier periods form a natural number system that exte nds the algebraic numbers by adding constants coming from geometry and phy sics. Because there are countably many periods\, one would expect it to be possible to compute effectively in this number system. This would require an effective height function and the ability to separate periods of bound ed height\, neither of which are currently possible.\n\nIn this talk\, we introduce an effective height function for periods of quartic surfaces def ined over algebraic numbers. We also determine the minimal distance betwee n periods of bounded height on a single surface. We use these results to p rove heuristic computations of Picard groups that rely on approximations o f periods. Moreover\, we give explicit Liouville type numbers that can not be the ratio of two periods of a quartic surface. This is ongoing work wi th Pierre Lairez (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:20210419T101258Z UID:SFUQNTAG/16 DESCRIPTION:Title: The Tangent-Graeffe root finding algorithm\nby Michael Monagan (Simo n Fraser University) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstrac t\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 compu te them.\nQuestion: How fast can we compute the roots?\n\nThe most well kn own method is the Cantor-Zassenhaus algorithm from 1981.\nIt is implemente d in Maple and Magma. It does\, on average\, $O(M(d) \\log d \\log p)$\na rithmetic operations in the field where $M(d)$ is the cost of multiplying two \npolynomials of degree $\\le d$.\n\nIn 2015 Grenet\, van der Hoeven a nd Lecerf found a beautiful new method for \nthe case $p = s 2^k + 1$ with $s \\in O(d)$.\nThe new method improves on Cantor-Zassenhaus by a factor of $O(\\log d)$.\nOur contribution is a speed up for the core computation of the new\nmethod by a constant factor and a C implementation of the new method\nusing asymptotically fast polynomial arithmetic.\n\nIn the talk I will present the main ideas behind the new Tangent-Graeffe algorithm\,\nso me timings comparing the Tangent Graeffe algorithm with the Cantor-Zassenh aus \nalgorithm 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:20210419T101258Z UID:SFUQNTAG/17 DESCRIPTION:Title: Products and Polarizations of Super-Isolated Abelian Varieties\nby S tefano Marseglia (Utrecht University) as part of SFU Quarantined NT-AG Sem inar\n\n\nAbstract\nSuper-isolated abelian varieties are abelian varieties over finite fields whose isogeny class contains a single isomorphism clas s. In this talk we will review their properties\, consider their products and\, in the ordinary case\, we will describe their (principal) polarizati ons.\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:20210419T101258Z UID:SFUQNTAG/18 DESCRIPTION:Title: On the irrationality of moduli spaces of K3 surfaces\nby Daniele Ago stini (MPI MiS) as part of SFU Quarantined 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 infinitel y many examples\,\nthe degree of irrationality is bounded polynomially in terms of g\, so that these spaces become more \nirrational\, but not too f ast. The key insight is that the irrationality is bounded by the coefficie nts \nof a certain modular form of weight 11. This is joint work with Igna cio Barros and 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:20210419T101258Z UID:SFUQNTAG/19 DESCRIPTION:Title: Top Weight Cohomology of $A_g$\nby Madeline Brandt (Brown University ) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nI will discuss a recent project in computing the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for sma ll values of $g$. This piece of the cohomology is controlled by the combin atorics of the boundary strata of a compactification of $A_g$. Thus\, it c an be computed combinatorially. This is joint work with Juliette Bruce\, M elody 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:20210419T101258Z 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 Quarantined NT-AG Seminar\n\n\nAbstract\nElliptic curves defined over the rational nu mbers arise from \ncertain modular forms. This is the celebrated Modularit y theorem of Wiles \net al. Prior to this development\, Ribet had proved a level lowering \ntheorem\, thanks to which one is able to optimize the le vel of the modular \nform in question. Ribet's theorem combined with the m odularity theorem of \nWiles together imply Fermat's Last theorem.\n\nIn j oint work with Ravi Ramakrishna\, we develop some new techniques to\nprove level lowering 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:20210419T101258Z UID:SFUQNTAG/21 DESCRIPTION:Title: Catastrophe discriminants of tensegrity frameworks\nby Alex Heaton ( The Fields Institute) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstra ct\nWe discuss elastic tensegrity frameworks made from rigid bars and elas tic cables\, depending on many parameters. For any fixed parameter values\ , the stable equilibrium position of the framework is determined by minimi zing an energy function subject to algebraic constraints. As parameters sm oothly change\, it can happen that a stable equilibrium disappears. This l oss of equilibrium is called `catastrophe' since the framework will experi ence large-scale shape changes despite small changes of parameters. Using nonlinear algebra we characterize a semialgebraic subset of the parameter space\, the catastrophe set\, which detects the merging of local extrema f rom this parametrized family of constrained optimization problems\, and he nce detects possible catastrophe. Tools from numerical nonlinear algebra a llow reliable and efficient computation of all stable equilibrium position s 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:20210419T101258Z UID:SFUQNTAG/22 DESCRIPTION:Title: Del Pezzo fibrations in positive characteristic\nby Andrea Fanelli a s part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nIn this talk\, I wi ll discuss some pathologies for the generic fibre of del Pezzo fibrations in characteristic $p>0$\, \nmotivated by the recent developments of the MM P in positive characteristic. The recent joint work with \nStefan Schröer applies to deduce information on the structure of 3-dimensional Mori fibr e 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:20210419T101258Z UID:SFUQNTAG/23 DESCRIPTION:Title: Hidden Variables in Linear Causal Models\nby Elina Robeva (Universit y of British Columbia) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstr act\nIdentifying causal relationships between random variables from observ ational data is an important hard problem in many areas of data science. T he presence of hidden variables\, though quite realistic\, pauses a variet y of further problems. Linear structural equation models\, which express e ach variable as a linear combination of all of its parent variables\, have long been used for learning causal structure from observational data. Sur prisingly\, when the variables in a linear structural equation model are n on-Gaussian the full causal structure can be learned without interventions \, while in the Gaussian case one can only learn the underlying graph up t o a Markov equivalence class. In this talk\, we first discuss how one can use high-order cumulant information to learn the structure of a linear non -Gaussian structural equation model with hidden variables. While prior wor k posits that each hidden variable is the common cause of two observed var iables\, we allow each hidden variable to be the common cause of multiple observed variables. Next\, we discuss hidden variable Gaussian causal mode ls and the difficulties that arise with learning those. We show it is hard to even describe the Markov equivalence classes in this case\, and we giv e a semi algebraic 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:20210419T101258Z 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 Quarantined NT-AG Seminar\n\n\nAbstract\nLet X be a smooth subvariety of $\\mathbb{P}^ n$ defined over a field k. Suppose k is an infinite field\, then the class ical theorem of Bertini asserts that X admits a smooth hyperplane section. However\, if k is a finite field\, there are examples of X such that ever y hyperplane H in $\\mathbb{P}^n$ defined over k is tangent to X. One of t he remedies in this situation is to extending the ground field k to its fi nite extension\, and considering all the hyperplanes defined over the exte nsion field. Then one can ask: Knowing the invariants of X (e.g. the degre e of X)\, how much one needs to extend k in order to guarantee at least o ne transverse hyperplane section? In this talk we will report several resu lts regarding to this type of questions. We also want to talk about a spec ial type of varieties (Frobenius nonclassical varieties) that appear natur ally in our research. This is a joint work with Shamil Asgarli and Kuan-We n 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:20210419T101258Z 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 Quarantined NT-AG Semin ar\n\n\nAbstract\nCurves over finite fields with many rational points have been of interest for both theoretical reasons and for applications. To ob tain such curves with large genus various methods have been employed in th e past. One such method is by means of explicit recursive equations and wi ll be the emphasis of this talk. The recursive nature of these towers make s them very special and in fact all good examples have been shown to have a modular interpretation of some sort. In this talk I will try to give an overview of the landscape of explicit recursive towers and their modularit y.\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:20210419T101258Z UID:SFUQNTAG/26 DESCRIPTION:Title: The local-global principle for quadratic forms over function fields\ nby Asher Auel (Dartmouth College) as part of SFU Quarantined NT-AG Semina r\n\n\nAbstract\nThe Hasse-Minkowski theorem says that a quadratic form ov er a global field admits a nontrivial zero if it admits a nontrivial zero everywhere locally. Over more general fields of arithmetic and geometric i nterest\, the failure of the local-global principle is often controlled by auxiliary structures of interest\, such as torsion points of the Jacobian and the Brauer group. I will explain work with V. Suresh on the failure of the local-global principle for quadratic forms over function fields var ieties of dimension at least two. The counterexamples we construct are co ntrolled by higher unramified cohomology groups and involve the study of C alabi-Yau varieties of generalized Kummer type that originally arose from number theory. Along the way\, we need to develop an arithmetic version o f a result of 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:20210419T101258Z 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 Quarantined NT-AG Seminar\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 fa mily of $A$\, is equal to 2. As a corollary\, the average $\\mathbb{Z}[\ \zeta]$-rank of $A_d$ is at most 1/2\, and at least 50% of $A_d$ have rank 0. More generally\, we prove average rank bounds for various twist f amilies of abelian varieties with "cyclotomic" multiplication (not necessa rily CM) over $\\bar F$\, such as sextic twist families of trigonal Jacobi ans over $\\mathbb{Q}$. These results have application to questions of " rank gain" for a fixed elliptic curve over a family of sextic fields\, as well as the distribution of $\\#C_d(F)$\, as $C_d$ varies through twists o f a fixed curve $C$ of genus $ g > 1$. This is joint work with Ariel Wei ss.\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:20210419T101258Z UID:SFUQNTAG/28 DESCRIPTION:Title: KP Solitons from Tropical Limits\nby Claudia Fevola (MPI MiS) as par t of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nIn this talk\, we presen t solutions to the Kadomtsev-Petviashvili equation whose underlying algebr aic curves undergo tropical degenerations. Riemann’s theta function beco mes a finite exponential sum that is supported on a Delaunay polytope. We introduce the Hirota variety which parametrizes all tau functions arising from such a sum. After introducing solitons solutions\, we compute tau fun ctions from points on the Sato Grassmannian that represent Riemann-Roch sp aces.\nThis is joint work with Daniele Agostini\, Yelena Mandelshtam and B ernd Sturmfels.\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:20210419T101258Z UID:SFUQNTAG/29 DESCRIPTION:Title: On Gröbner bases over Tate algebras\nby Tristan Vaccon (Université de Limoges) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nTate series are a generalization of polynomials introduced by John Tate in 1962 \, when defining a p-adic analogue of the correspondence between algebraic geometry and analytic geometry. This p-adic analogue is called rigid geom etry\, and Tate series\, similar to analytic functions in the complex case \, are its fundamental objects. Tate series are defined as multivariate fo rmal power series over a p-adic ring or field\, with a convergence conditi on on a closed ball.\n\nTate series are naturally approximated by multivar iate polynomials over F_p or Z/p^n Z\, and it is possible to define a theo ry of Gröbner bases for ideals of Tate series\, which opens the way towar ds effective rigid geometry. \n\nIn this talk\, I will present classical a lgorithms to compute Gröbner bases (Buchberger\, F5\, FGLM) and how they can be adapted for Tate series.\n\nJoint work with Xavier Caruso and Thib aut Verron.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/29/ END:VEVENT END:VCALENDAR