BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Caroline Matson DTSTART:20200929T201500Z DTEND:20200929T211500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/1 DESCRIPTION:Title: The commutant monoid of a higher-dimensional power ser ies map\nby Caroline Matson as part of Binghamton Arithmetic Seminar\n \n\nAbstract\nIn a 1994 paper\, Lubin examined nonarchimedean dynamical sy stems\, or families of power series that commute under composition. He def ined a stable power series to be a power series f(x) = bx + (higher degree terms) such that the linear coefficient b is neither zero nor a root of u nity and showed that if f(x) is stable then for any constant c there exist s a unique power series g(x) such that f(g(x) = g(f(x)) and g(x) = cx + (h igher degree terms). In this talk we will generalize this problem to multi ple dimensions and will explore the notion of stability in this more compl icated setting.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:K. V. Shuddhodan (Purdue University) DTSTART:20210920T201500Z DTEND:20210920T211500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/2 DESCRIPTION:Title: The (non-uniform) Hrushovski-Lang-Weil estimates\n by K. V. Shuddhodan (Purdue University) as part of Binghamton Arithmetic S eminar\n\n\nAbstract\nIn 1996 using techniques from model theory and inter section theory\, Hrushovski obtained a generalisation of the Lang-Weil est imates. Subsequently\, the estimate has found applications in group theory \, algebraic dynamics\, and algebraic geometry. We shall discuss an l-adic proof of the non-uniform version of these estimates and also the rational ity of the associated generating function.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Joe Kramer-Miller DTSTART:20211109T213000Z DTEND:20211109T223000Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/3 DESCRIPTION:Title: Ramification of geometric p-adic representations in po sitive characteristic\nby Joe Kramer-Miller as part of Binghamton Arit hmetic Seminar\n\n\nAbstract\nA classical theorem of Sen describes a close relationship between the ramification filtration and the p-adic Lie filtr ation for p-adic representations in mixed characteristic. Unfortunately\, Sen's theorem fails miserably in positive characteristic. The extensions a re just too wild! There is some hope if we restrict to representations com ing from geometry. Let X be a smooth variety and let D be a normal crossin g divisor in X and consider a geometric p-adic lisse sheaf on X-D (e.g. th e p-adic Tate module of a fibration of abelian varieties). We show that th e Abbes-Saito conductors along D exhibit a remarkable regular growth with respect to the p-adic Lie filtration.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sunil Chetty DTSTART:20211102T201500Z DTEND:20211102T211500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/4 DESCRIPTION:Title: Selmer groups and ranks of elliptic curves\nby Sun il Chetty as part of Binghamton Arithmetic Seminar\n\n\nAbstract\nIn the t heory of elliptic curves\, understanding the behavior of\nrank is a centra l problem. In light of the Birch-Swinnerton-Dyer and\nTate-Shafarevich Con jectures\, there are three avenues for understanding\nrank of a given elli ptic curve E/K: by the structure of the Mordell-Weil\ngroup E(K)\, by the vanishing of the associated L-function L(E/K\,s)\, or by\nthe structure of the associated Selmer group Sel{E}{K}. We will discuss\nsome of the big i deas for attacking the rank problem over number fields via\nthe Selmer gro up approach\, as well as methods of comparing parallel tools\nin the L-fun ction approach.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Guiilermo Mantilla Soler DTSTART:20211116T211500Z DTEND:20211116T221500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/5 DESCRIPTION:Title: Applications of Higher composition laws to the classif ication of number fields\nby Guiilermo Mantilla Soler as part of Bingh amton Arithmetic Seminar\n\n\nAbstract\nIn this talk we will describe what natural invariants we have studied with the aim of characterizing number fields\, and how some of those are related to the higher composition laws discovered by Bhargava at the beginning of this century.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Pietromonaco DTSTART:20220329T201500Z DTEND:20220329T211500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/6 DESCRIPTION:Title: The enumerative geometry of orbifold K3 surfaces\n by Stephen Pietromonaco as part of Binghamton Arithmetic Seminar\n\n\nAbst ract\nA few of the most celebrated theorems in enumerative geometry (both predicted by string theorists) surround curve-counting for K3 surfaces. Th e Yau-Zaslow formula computes the honest number of rational curves in a K3 surface\, and was generalized to the Katz-Klemm-Vafa formula computing th e (virtual) number of curves of any genus. In this talk\, I will review th is story and then describe a recent generalization to orbifold K3 surfaces . One interpretation of the new theory is as producing a virtual count of curves in the orbifold\, where we track both the genus of the curve and th e genus of the corresponding invariant curve upstairs. As one example\, we generalize the counts of hyperelliptic curves in an Abelian surface carri ed out by Bryan-Oberdieck-Pandharipande-Yin. This is work in progress with Jim Bryan.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Xuqiang Qin DTSTART:20220419T201500Z DTEND:20220419T211500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/7 DESCRIPTION:Title: Birational geometry of the Mukai system on a K3 surfac e\nby Xuqiang Qin as part of Binghamton Arithmetic Seminar\n\n\nAbstra ct\nThe Mukai system on a K3 surface is a moduli space of torsion\nsheaves \, admitting a Lagrangian fibration given by mapping each sheaf to\nits su pport. In this talk\, we will focus on a class of Mukai systems which\nare birational to Hilbert scheme of points. Using the wall crossing\ntechniqu e from Bridgeland stability\, we decompose the birational map into a\nsequ ence of flops. As a result\, we give a full description of the\nbirational geometry of such a Mukai system. This is based on joint work\nwith Justin Sawon.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Aranya Lahiri DTSTART:20220510T201500Z DTEND:20220510T211500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/8 DESCRIPTION:Title: Irreducibility of rigid analytic vectors in p-adic pri ncipal series representations\nby Aranya Lahiri as part of Binghamton Arithmetic Seminar\n\n\nAbstract\nFor the $L$-rational points $G:=\\mathbb {G}(L)$ of a p-adic\nreductive group\, let $Ind^G_B(\\chi)$ be the conti nuous p-adic principal\nseries representations. Here $L$ is a finite exten sion of $\\mathbb{Q}_p$\,\n $B$ is the Borel subgroup corresponding to a m aximal torus $T$ and $\\chi$\nis a character of $T$. We will consider the globally analytic vectors of\nthe pro-p Iwahori group $I$ in the principa l series representations. This\nis done by endowing the pro-p Iwahori wit h a $p$-valuation and subsequently\ngiving it a structure of a rigid analy tic group\, thus generalizing the work\nof Lazard. The main result of this talk will be the topological\nirreducibility of these globally analytic v ectors under certain assumptions\non $\\chi$. This is a generalization of works of Clozel and Ray in the case\nof $G:= GL_n(L)$. This is joint work with Claus Sorensen.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Haiyang Wang (University of Georgia) DTSTART:20240312T201500Z DTEND:20240312T211500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/9 DESCRIPTION:Title: Elliptic curves with potentially good supersingular re duction and coefficients of the classical modular polynomials\nby Haiy ang Wang (University of Georgia) as part of Binghamton Arithmetic Seminar\ n\n\nAbstract\nLet $O_K$ be a Henselian discrete valuation domain with fie ld of fractions $K$. Assume that $O_K$ has algebraically closed residue fi eld $k$. Let $E/K$ be an elliptic curve with additive reduction. The semi- stable reduction theorem asserts that there exists a minimal extension $L/ K$ such that the base change $E_L/L$ has semi-stable reduction. It is natu ral to wonder whether specific properties of the semi-stable reduction and of the extension $L/K$ impose restrictions on what types of Kodaira type the special fiber of $E/K$ may have. \n\nIn this talk we will discuss the restrictions imposed on the reduction type when the extension $L/K$ is wi ldly ramified of degree 2\, and the curve $E/K$ has potentially good super singular reduction. We will also talk about the possible reduction types o f two isogenous elliptic curves with these properties and its relation to the congruence properties of the coefficients of the classical modular pol ynomials.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Shane Chern (Dalhousie University) DTSTART:20240319T201500Z DTEND:20240319T211500Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/10 DESCRIPTION:Title: The Seo-Yee conjecture: Nonmodular infinite products\ , seaweed algebras\, and integer partitions\nby Shane Chern (Dalhousie University) as part of Binghamton Arithmetic Seminar\n\n\nAbstract\nIn th is talk\, I will present my recent work on the Seo-Yee conjecture\, which claims the nonnegativity of coefficients in the expansion of a q-series in finite product. The Seo-Yee conjecture arises from the study of seaweed al gebras (a special type of Lie algebra)\, and is closely tied with the enum eration of the index statistic of integer partitions. Our proof of the Seo -Yee conjecture is built upon the asymptotic analysis for a generic family of nonmodular infinite products near each root of unity.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Anitha Srinivasan (Universidad Pontificia Comillas\, Madrid) DTSTART:20260317T200000Z DTEND:20260317T210000Z DTSTAMP:20260422T215403Z UID:BinghamtonArithmeticSeminar/11 DESCRIPTION:Title: The generalized Markoff equation\nby Anitha Srin ivasan (Universidad Pontificia Comillas\, Madrid) as part of Binghamton Ar ithmetic Seminar\n\n\nAbstract\nThe talk will look at various aspects of the generalized Markoff equation $a^2+b^2+c^2=3abc+m$ ($m\\ge 0$)\, giving an overview of all the exciting work in the area. A few examples of topi cs that will be mentioned are: the classification of solution triples $(a\ , b\, c)$ that come from $k$-Fibonacci sequences\, open conjectures (whic h $m's$ have no solutions?)\, counting algorithms for the number of soluti ons (trees) and the Markoff equation mod $p$.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/11/ END:VEVENT END:VCALENDAR