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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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:20220528T080636Z 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 BEGIN:VEVENT SUMMARY:Özlem Ejder (Boğaziçi University) DTSTART;VALUE=DATE-TIME:20210527T163000Z DTEND;VALUE=DATE-TIME:20210527T173000Z DTSTAMP;VALUE=DATE-TIME:20220528T080636Z UID:SFUQNTAG/30 DESCRIPTION:Title: Galois theory of Dynamical Belyi Maps\nby Özlem Ejder (Boğaziçi U niversity) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nLet $f: \\mathbb{P}^1_K \\rightarrow \\mathbb{P}^1_K$ be a rational map defined o ver 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 dyna mics. In this talk\, we will discuss the various Galois groups attached to the iterates of $f$\, namely arithmetic and geometric monodromy groups an d Arboreal Galois representations. While providing a survey of recent resu lts on the subject\, 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:20220528T080636Z UID:SFUQNTAG/31 DESCRIPTION:Title: Projections in toric degenerations and standard monomials\nby Lara B ossinger (Instituto de Matemáticas UNAM) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nI will report on joint work in progress with Takuy a Murata. We study toric degenerations\, i.e. flat morphism of a normal va riety to the affine line whose generic fibre is isomorphic to a fixed proj ective variety and whose special fibre is a projective toric variety. Alth ough such a flat morphism may be given abstractly (i.e. without an embeddi ng\, for example a toric scheme over the affine line) using valuations and Gröbner theory we may restrict our attention to the case where our famil y comes endowed with an embedding. I will illustrate an example of an elli ptic curve where a toric degeneration admits a projection from the generic fibre (the elliptic curve) to the special fibre (the toric curve). We wan t to understand 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 degenerati ons.\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:20220528T080636Z UID:SFUQNTAG/32 DESCRIPTION:Title: Counting elliptic curves with a rational N-isogeny\nby Soumya Sankar (Ohio State University) as part of SFU Quarantined NT-AG Seminar\n\n\nAbs tract\nThe classical problem of counting elliptic curves with a rational N -isogeny can be phrased in terms of counting rational points on certain mo duli stacks of elliptic curves. Counting points on stacks poses various ch allenges\, and I will discuss these along with a few ways to overcome them . I will also talk about the theory of heights on stacks developed in rece nt work of Ellenberg\, Satriano and Zureick-Brown and use it to count elli ptic curves with an N-isogeny for certain N. The talk assumes no prior kno wledge of stacks 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:20220528T080636Z 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 Quarantined NT -AG Seminar\n\n\nAbstract\nThere are two plane quadrics passing through fo ur general points and tangent to one general line. There are six ways to p roperly color vertices of a triangle with three colors. The maximum likeli hood function for a general linear concentration two dimensional model in a four dimensional space has three critical points. Each of these examples of course comes naturally in families.\nIn our talk we will try to explai n what the above numbers mean\, how to compute them and that they are all shadows of the same construction. Our methods are based on the cohomology ring of the so-called variety of complete forms.\nThe talk is based on wor ks with Conner\, Dinu\, Manivel\, Monin\, Seynnaeve\, Wisniewski and Vodic ka. These are on the other hand based on fundamental works due to Huh\, Pr agacz\, Sturmfels\, 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:20220528T080636Z 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 Quarantined NT-AG Seminar\n\n\nAbstract\nPhysicists Arkhani-Hamed an d Trnka introduced the amplituhedron to better understand scattering ampli tudes in N=4 super Yang-Mills theory. The amplituhedron is the image of th e totally nonnegative Grassmannian under the "amplituhedron map"\, which i s induced by matrix multiplication. Examples of amplituhedra include cycli c polytopes\, the totally nonnegative Grassmannian itself\, and cyclic hyp erplane arrangements. In general\, the amplituhedron is not a polytope. Ho wever\, Lukowski--Parisi--Williams noticed a mysterious connection between the m=2 amplituhedron and the hypersimplex\, and conjectured a correspond ence between their fine positroidal subdivisions. I'll discuss joint work with Matteo Parisi and Lauren Williams\, in which we prove one direction o f this correspondence. Along the way\, we prove an intrinsic description o f the m=2 amplituhedron conjectured by Arkhani-Hamed--Thomas--Trnka\; give a decomposition of the m=2 amplituhedron into Eulerian number-many sign c hambers\, in direct analogy to a triangulation of the hypersimplex\; and f ind new cluster 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:20220528T080636Z UID:SFUQNTAG/35 DESCRIPTION:Title: Blow-Up Algebras of Strongly Stable Ideals\nby Selvi Kara (Universit y of South Alabama) as part of SFU Quarantined 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 collection of ideals encode many algebraic properties of these id eals\, 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 connection\, Rees and multi-Rees algebras are also called blow-up al gebras in the literature.\n\nIn this talk\, we will focus on Rees and mult i-Rees algebras of strongly stable ideals. In particular\, we will discuss the Koszulness of these algebras through a systematic study of these obje cts via three parameters: the number of ideals in the collection\, the num ber of Borel generators of each ideal\, and the degrees of Borel generator s. In our study\, we utilize combinatorial objects such as fiber graphs to detect Gröbner bases and Koszulness of these algebras. This talk is base d 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:20220528T080636Z UID:SFUQNTAG/36 DESCRIPTION:Title: Primary decomposition with differential operators.\nby Yairon Cid-Ru iz (Ghent University) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstra ct\nWe introduce differential primary decompositions for ideals in a commu tative ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the arithmetic multiplicity. M inimal differential primary decompositions are unique up to change of base s. Our results generalize the construction of Noetherian operators for pri mary ideals in the analytic theory of Ehrenpreis-Palamodov\, and they offe r a concise method for representing affine schemes. The case of modules is also addressed. 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:20220528T080636Z 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 Quarantined NT- AG Seminar\n\n\nAbstract\nAn elliptic curve defined over the rationals giv es rise to a \ncompatible system of Galois representations. The Iwasawa in variants \nassociated to these representations epitomize their arithmetic and Iwasawa \ntheoretic properties. The study of these invariants is the s ubject of much \nconjecture and contemplation. For instance\, according to a long-standing \nconjecture of R. Greenberg\, the Iwasawa "mu-invariant" must vanish\, subject \nto mild hypothesis. Overall\, there is a subtle r elationship between the \nbehavior of these invariants and the p-adic Birc h and Swinnerton-Dyer \nformula. We study the behaviour of these invariant s on average\, where \nelliptic curves over the rationals are ordered acco rding to height. I will \ndiscuss some recent results (joint with Debanjan a Kundu) in which we set \nout new directions in arithmetic statistics and Iwasawa theory.\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:20220528T080636Z 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 Quarantined NT-AG Seminar\n\n\nAbstract\nWe present a combinat orial algorithm on trivalent trees that we call a lazy tournament\, which gives rise to a new geometric interpretation of the multidegrees of a proj ective embedding 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 boundary points of the moduli space that can be seen to total (2n- 7)!!\, giving a natural proof of the value of the total degree. These set s are compatible with the forgetting maps used to derive the previously kn own recursion for the multidegrees.\n\nAs time permits\, we will discuss a n alternative combinatorial construction of (non-disjoint) sets of boundar y points that enumerate the multidegrees\, via slide rules\, that can in f act be achieved geometrically via a degeneration of intersections with hyp erplanes in the projective embedding. These combinatorial rules further g eneralize to give a positive expansion of any product of psi or omega clas ses on M_{0\,n}-bar in terms of boundary strata.\n\nThis is joint work wit h Sean Griffin 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:20220528T080636Z UID:SFUQNTAG/39 DESCRIPTION:Title: Alternative compactifications of the moduli space of curves\nby Vanc e Blankers (Northeastern University) as part of SFU Quarantined NT-AG Semi nar\n\n\nAbstract\nThe moduli space of curves is an important object in mo dern algebraic geometry\, both interesting in its own right and serving as a test space for broader geometric programs. These often require the spac e to be compact\, which leads to a variety of choices for compactification \, the most well-known of which is the Deligne-Mumford-Knudsen compactific ation by stable curves\, originally introduced in 1969. Since then\, sever al alternative compactifications have been constructed and studied\, and i n 2013 David Smyth used a combinatorial framework to make progress towards classifying all "sufficiently nice" compactifications. In this talk\, I'l l discuss some of the most well-studied compactifications\, as well as two new compactifications\, which together classify the Gorenstein compactifi cations in genus 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:20220528T080636Z UID:SFUQNTAG/40 DESCRIPTION:Title: Unbounded negativity on rational surfaces in positive characteristic \nby Raymond Cheng (Columbia University) as part of SFU Quarantined 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? Apparen tly\, there are situations in which curves might not actually get so negat ive: an old folklore conjecture\, nowadays known as the Bounded Negativity Conjecture\, predicts that if S were defined over the complex numbers\, t hen the self-intersection of any curve in S is bounded below by a constant depending only on S. If\, however\, S were defined over a field of positi ve characteristic\, then it is known that the Bounded Negativity Conjectur e as stated cannot hold. For a long time\, however\, it was not known whet her the Conjecture failed for rational surfaces in positive characteristic . In this talk\, I describe the first examples of rational surfaces failin g Bounded Negativity which I constructed with Remy van Dobben de Bruyn ear lier this year.\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:20220528T080636Z 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 Quaran tined NT-AG Seminar\n\n\nAbstract\nAn order $\\mathcal{O}$ in an algebraic number field is called monogenic if over $\\mathbb{Z}$ it can be generate d by one element. Győry has shown that there are finitely equivalence cla sses $\\alpha \\in \\mathcal{O}$ such that $\\mathcal{O} = \\mathbb{Z}[\\a lpha]$\, where two algebraic integers $\\alpha\, \\alpha'$ are called equi valent if $\\alpha + \\alpha'$ or $\\alpha - \\alpha'$ is a rational integ er. An interesting problem is to count the number of monogenizations of a given monogenic order. First we will note\, for a given order $\\mathcal{O }$\, that $$\\mathcal{O} = \\mathbb{Z}[\\alpha] \\text{ in } \\alpha$$ is indeed a Diophantine equation. Then we will discuss how some old algorithm ic results can be used to obtain new and improved upper bounds for the num ber of monogenizations of a cubic or quartic order.\n\nThis talk should be accessible to any math graduate student and\nquestions about basic concep ts are welcome. We will start by recalling\nsome definitions from elementa ry 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:20220528T080636Z 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 Quarantined NT-A G Seminar\n\n\nAbstract\nKazhdan-Lusztig varieties are defined by ideals g enerated by certain minors of a matrix\, which are chosen by a combinatori al rule. These varieties are of interest in commutative algebra and Schube rt varieties. Each Kazhdan-Lusztig variety has a natural torus action from which one can construct a cone. The complexity of this torus action can b e computed from the dimension of the cone and\, in some sense\, indicates how close the variety is to the toric variety of the cone. In joint work w ith Maria Donten-Bury and Irem Portakal we address the problem of classify ing which Kazhdan-Lusztig varieties have a given complexity. We do so by u tilizing 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:20220528T080636Z 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 Quarantined NT-AG S eminar\n\nLecture held in AQ 4145.\n\nAbstract\nLet $L/K$ be a Galois exte nsion of number fields such that $L\\not=\\mathbb{Q}$\, and let $C$ be a c onjugacy class in the Galois group of $L/K$. We show that there exists an unramified prime $\\mathfrak{p}$ of $K$ such that $\\sigma_{\\mathfrak{p}} =C$ and $N \\mathfrak{p} \\le d_{L}^{B}$ with $B= 310$. This improves a pr evious result of Ahn and Kwon\, who showed that $B=12\\\,577$ is admissibl e. The main tool is a stronger Deuring-Heilbronn (zero-repulsion) phenomen on. We also use Fiori's numerical verification for a finite list of fields . This is joint 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:20220528T080636Z UID:SFUQNTAG/45 DESCRIPTION:Title: Brill--Noether Theory over the Hurwitz space\nby Isabel Vogt (Brown University) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nLet C be a curve of genus g. A fundamental problem in the theory of algebraic cu rves is to understand maps of C to projective space of dimension r of degr ee d. When the curve C is general\, the moduli space of such maps is well- understood by the main theorems of Brill--Noether theory. However\, in na ture\, curves C are often encountered already equipped with a map to some projective space\, which may force them to be special in moduli. The simp lest case is when C is general among curves of fixed gonality. Despite mu ch study over the past three decades\, a similarly complete picture has pr oved elusive in this case. In this talk\, I will discuss joint work with E ric Larson and Hannah Larson that completes such a picture\, by proving an alogs 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:20220528T080636Z 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 Quarantined NT-AG Seminar\n\n\nAbstract\nWe will first talk about the Cere sa class\, which is the image under a cycle class map of a canonical algeb raic cycle associated to a curve in its Jacobian. This class vanishes for all hyperelliptic curves and was expected to be nonvanishing for non-hyper elliptic curves. In joint work with Dean Bisogno\, Wanlin Li and Daniel Li tt\, we construct a non-hyperelliptic genus 3 quotient of the Fricke-Macbe ath curve with vanishing Ceresa class\, using the character theory of the automorphism group of the curve\, namely\, PSL_2(F_8). This will also incl ude the tale of another explicit genus 3 curve studied by Schoen that was lost and then found again!\n\nTime permitting\, we will also talk about so me Galois cohomology classes that obstruct the existence of rational point s on curves\, by obstructing splittings to natural exact sequences coming from the fundamental group of a curve. In joint work with Wanlin Li\, Dani el Litt and Nick Salter\, we use these obstruction classes to give a new p roof of Grothendieck’s section conjecture for the generic curve of genus g > 2. An analysis of the degeneration of these classes at the boundary o f the moduli space of curves\, combined with a specialization argument let s us prove the existence of infinitely many curves of each genus over p-ad ic fields and 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:20220528T080636Z UID:SFUQNTAG/47 DESCRIPTION:Title: Cluster algebras and deformation theory\nby Nathan Ilten (Simon Fras er University) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nClu ster Algebras\, introduced in 2001 by Fomin and Zelevinsky\, are a kind of commutative ring equipped with special combinatorial structure. They appe ar in a range of contexts\, from representation theory to mirror symmetry. After providing a gentle introduction to cluster algebras\, I will report on one aspect of work-in-progress with Alfredo Nájera Chávez and Hipoli to Treffinger. We show that for cluster algebras of finite type\, the clus ter algebra with universal coefficients is equal to a canonically identifi ed subfamily of the semiuniversal family for the Stanley-Reisner ring of t he cluster complex.\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:20220528T080636Z UID:SFUQNTAG/51 DESCRIPTION:Title: Moments of the Riemann zeta function\nby Nathan Ng (University of Le thbridge) as part of SFU Quarantined 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 critical line have been extensively studied. In 1918 Hardy-Littlew ood established an asymptotic formula for the second moment ($k=1$) and in 1926 Ingham established an asymptotic formula for the fourth moment $(k=2 )$. Since then no other moments have been asymptotically evaluated. In th e 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 for mula for the sixth moment ($k=3$) follows from a conjectural formula for s ome ternary additive divisor sums. In this talk I will give an overview o f these results.\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:20220528T080636Z UID:SFUQNTAG/52 DESCRIPTION:Title: Integrality of $G$-local systems\nby Christian Klevdal (University o f Utah) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nSimpson co njectured that for a reductive group $G$\, rigid $G$-local systems on a sm ooth projective complex variety are integral. I will discuss a proof of in tegrality for cohomologically rigid $G$-local systems. This generalizes an d is inspired by work of Esnault and Groechenig for $GL_n$. Surprisingly\, the main tools used in the proof (for general $G$ and $GL_n$) are the wor k of L. Lafforgue on the Langlands program for curves over function fields \, and work of Drinfeld on companions of $\\ell$-adic sheaves. The major d ifferences between general $G$ and $GL_n$ are first to make sense of compa nions 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 Pat rikis.\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:20220528T080636Z UID:SFUQNTAG/53 DESCRIPTION:Title: Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials\nby Patricia Klein (University of Minnesota) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nKnutson and Miller established a connection b etween the anti-diagonal Gröbner degenerations of matrix Schubert varieti es and the pre-existing combinatorics of pipe dreams. They used this corre spondence to give a geometrically-natural explanation for the appearance o f the combinatorially-defined Schubert polynomials as representatives of S chubert classes. In this talk\, we will describe a similar connection betw een diagonal degenerations of matrix Schubert varieties and bumpless pipe dreams\, newer combinatorial objects introduced by Lam\, Lee\, and Shimozo no. This connection 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:20220528T080636Z 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 Quarantined NT-AG Seminar\n\n\nAbstract\nA line bundle is k-jet ample if it has enough global sections to separate points\, tangent vector s\, and also their higher order analogues called k-jets. For example\, 0-j et ampleness is equivalent to global generation and 1-jet ampleness is equ ivalent to very ampleness. We give sharp bounds guaranteeing that a line b undle on a projective toric variety is k-jet ample in terms of its interse ction numbers with the invariant curves\, in terms of the lattice lengths of the edges of its polytope\, in terms of the higher concavity of its pie cewise linear function and in terms of its Seshadri constant. As an applic ation\, we prove the k-jet generalizations of Fujita’s conjectures on to ric varieties.\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:20220528T080636Z UID:SFUQNTAG/57 DESCRIPTION:Title: Bott periodicity from algebraic geometry\nby Jim Bryan (University o f British Columbia) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract \nA famous theorem in algebraic topology is Bott periodicity: the homotopy groups of the space of orthogonal matrices repeat with period 8: pi_k(O) = pi_{k+8}(O) . I will give an elementary overview of Bott periodicity an d then I will explain how to formulate and prove a theorem in algebraic ge ometry which\, when specialized to the field of complex numbers\, recovers the usual topological Bott periodicity\, but makes sense over any field. This is work in progress with Ravi Vakil.\n LOCATION:https://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:20220528T080636Z 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 Quarantined 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 i nvolutions of hyperkahler manifolds of Kummer type. The fixed loci of thes e involutions correspond to cohomology classes and have very interesting p roperties. The 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:20220528T080636Z UID:SFUQNTAG/60 DESCRIPTION:Title: Multigraded regularity on products of projective spaces\nby Juliette Bruce (University of California\, Berkeley) as part of SFU Quarantined NT -AG Seminar\n\n\nAbstract\nEisenbud and Goto described the Castelnuovo-Mum ford regularity of a module on projective space in terms of three differen t properties of the corresponding graded module: its betti numbers\, its l ocal cohomology\, and its truncations. For the multigraded generalization of regularity defined by Maclagan and Smith\, these three conditions are n o longer equivalent. I will characterize each of them for modules on produ cts of projective 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:20220528T080636Z UID:SFUQNTAG/62 DESCRIPTION:Title: Enumerative Geometry of Orbifold K3 Surfaces\nby Stephen Pietromonac o (University of British Columbia) as part of SFU Quarantined NT-AG Semina r\n\nLecture held in K-9509.\n\nAbstract\nTwo of the most celebrated theor ems in enumerative geometry\n(both predicted by string theorists) surround curve-counting for K3\nsurfaces. The Yau-Zaslow formula computes the hone st 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 this talk\, I will\nreview this story and then describe a recent generalization to orbifold K3\nsurfaces. One interpretation of the new th eory is as producing a virtual\ncount of curves in the orbifold\, where we track both the genus of the curve\nand the genus of the corresponding inv ariant curve upstairs. As one\nexample\, we generalize the counts of hyper elliptic curves in an Abelian\nsurface carried out by Bryan-Oberdieck-Pand haripande-Yin. 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:20220528T080636Z 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 Quarantined NT-AG Seminar\n\n\nAbstract\nA variety satisfies potential density if it contains a dense subset of rational points after e xtending its ground field by a finite degree. A collection of varieties sa tisfies uniform potential density if that degree can be uniformly bounded. I will discuss this property for connected algebraic groups of a fixed di mension 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:20220528T080636Z UID:SFUQNTAG/64 DESCRIPTION:Title: Lattice Walk Enumeration: Analytic\, algebraic and geometric aspects \nby Marni Mishna (Simon Fraser University) as part of SFU Quarantined NT- AG Seminar\n\nLecture held in K-9509.\n\nAbstract\nThis talk will survey c lassification of lattice path models via their generating functions.. A ve ry classic object of combinatorics\, lattice walks withstand study from a variety of perspectives. Even the simple task of classifying the two dimen sional nearest neighbour walks restricted to the first quadrant has brough t 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 lattice walks can naturally guide the classification of functions into categories like algebraic\, D-finite\, differentiably algebraic and b eyond. Elliptic curves and differential Galois theory play an important r ole.\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:20220528T080636Z UID:SFUQNTAG/65 DESCRIPTION:Title: Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials\nby Patricia Klein (University of Minnesota) as part of SFU Quarantined NT-AG Seminar\n\n\nAbstract\nKnutson and Miller established a connection b etween the anti-diagonal Gröbner degenerations of matrix Schubert varieti es and the pre-existing combinatorics of pipe dreams. They used this corre spondence to give a geometrically-natural explanation for the appearance o f the combinatorially-defined Schubert polynomials as representatives of S chubert classes. In this talk\, we will describe a similar connection betw een diagonal degenerations of matrix Schubert varieties and bumpless pipe dreams\, newer combinatorial objects introduced by Lam\, Lee\, and Shimozo no. This connection 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:20220528T080636Z 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 Quarantined NT-AG Semi nar\n\n\nAbstract\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 l etters 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. T his talk includes joint work with Rob Silversmith.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/66/ END:VEVENT END:VCALENDAR