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:20260404T111102Z UID:BinghamtonArithmeticSeminar/1 DESCRIPTION:Title: The commutant monoid of a higher-dimensional po wer series map\nby Caroline Matson as part of Binghamton Arithmetic Se minar\n\n\nAbstract\nIn a 1994 paper\, Lubin examined nonarchimedean dynam ical systems\, or families of power series that commute under composition. He defined 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 ro ot of unity and showed that if f(x) is stable then for any constant c ther e exists a unique power series g(x) such that f(g(x) = g(f(x)) and g(x) = cx + (higher degree terms). In this talk we will generalize this problem t o multiple dimensions and will explore the notion of stability in this mor e complicated setting.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:K. V. Shuddhodan (Purdue University) DTSTART:20210920T201500Z DTEND:20210920T211500Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/2 DESCRIPTION:Title: The (non-uniform) Hrushovski-Lang-Weil estimate s\nby K. V. Shuddhodan (Purdue University) as part of Binghamton Arith metic Seminar\n\n\nAbstract\nIn 1996 using techniques from model theory an d intersection theory\, Hrushovski obtained a generalisation of the Lang-W eil estimates. 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 r ationality of the associated generating function.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Joe Kramer-Miller DTSTART:20211109T213000Z DTEND:20211109T223000Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/3 DESCRIPTION:Title: Ramification of geometric p-adic representation s in positive characteristic\nby Joe Kramer-Miller as part of Binghamt on Arithmetic Seminar\n\n\nAbstract\nA classical theorem of Sen describes a close relationship between the ramification filtration and the p-adic Li e filtration for p-adic representations in mixed characteristic. Unfortuna tely\, Sen's theorem fails miserably in positive characteristic. The exten sions are just too wild! There is some hope if we restrict to representati ons coming from geometry. Let X be a smooth variety and let D be a normal crossing divisor in X and consider a geometric p-adic lisse sheaf on X-D ( e.g. the p-adic Tate module of a fibration of abelian varieties). We show that the Abbes-Saito conductors along D exhibit a remarkable regular growt h with respect to the p-adic Lie filtration.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sunil Chetty DTSTART:20211102T201500Z DTEND:20211102T211500Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/4 DESCRIPTION:Title: Selmer groups and ranks of elliptic curves\ nby Sunil Chetty as part of Binghamton Arithmetic Seminar\n\n\nAbstract\nI n the theory of elliptic curves\, understanding the behavior of\nrank is a central problem. In light of the Birch-Swinnerton-Dyer and\nTate-Shafarev ich Conjectures\, there are three avenues for understanding\nrank of a giv en elliptic 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 struc ture of the associated Selmer group Sel{E}{K}. We will discuss\nsome of th e big ideas for attacking the rank problem over number fields via\nthe Sel mer group approach\, as well as methods of comparing parallel tools\nin th e L-function approach.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Guiilermo Mantilla Soler DTSTART:20211116T211500Z DTEND:20211116T221500Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/5 DESCRIPTION:Title: Applications of Higher composition laws to the classification of number fields\nby Guiilermo Mantilla Soler as part o f Binghamton Arithmetic Seminar\n\n\nAbstract\nIn this talk we will descri be what natural invariants we have studied with the aim of characterizing number fields\, and how some of those are related to the higher compositio n laws discovered by Bhargava at the beginning of this century.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Pietromonaco DTSTART:20220329T201500Z DTEND:20220329T211500Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/6 DESCRIPTION:Title: The enumerative geometry of orbifold K3 surface s\nby Stephen Pietromonaco as part of Binghamton Arithmetic Seminar\n\ n\nAbstract\nA few of the most celebrated theorems in enumerative geometry (both predicted by string theorists) surround curve-counting for K3 surfa ces. The Yau-Zaslow formula computes the honest number of rational curves in a K3 surface\, and was generalized to the Katz-Klemm-Vafa formula compu ting the (virtual) number of curves of any genus. In this talk\, I will re view this story and then describe a recent generalization to orbifold K3 s urfaces. One interpretation of the new theory is as producing a virtual co unt of curves in the orbifold\, where we track both the genus of the curve and the genus of the corresponding invariant curve upstairs. As one examp le\, we generalize the counts of hyperelliptic curves in an Abelian surfac e carried out by Bryan-Oberdieck-Pandharipande-Yin. This is work in progre ss with Jim Bryan.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Xuqiang Qin DTSTART:20220419T201500Z DTEND:20220419T211500Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/7 DESCRIPTION:Title: Birational geometry of the Mukai system on a K3 surface\nby Xuqiang Qin as part of Binghamton Arithmetic Seminar\n\n\ nAbstract\nThe Mukai system on a K3 surface is a moduli space of torsion\n sheaves\, admitting a Lagrangian fibration given by mapping each sheaf to\ nits support. In this talk\, we will focus on a class of Mukai systems whi ch\nare birational to Hilbert scheme of points. Using the wall crossing\nt echnique from Bridgeland stability\, we decompose the birational map into a\nsequence of flops. As a result\, we give a full description of the\nbir ational geometry of such a Mukai system. This is based on joint work\nwith Justin Sawon.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Aranya Lahiri DTSTART:20220510T201500Z DTEND:20220510T211500Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/8 DESCRIPTION:Title: Irreducibility of rigid analytic vectors in p-a dic principal series representations\nby Aranya Lahiri as part of Bing hamton 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 th e continuous p-adic principal\nseries representations. Here $L$ is a finit e extension of $\\mathbb{Q}_p$\,\n $B$ is the Borel subgroup corresponding to a maximal torus $T$ and $\\chi$\nis a character of $T$. We will consid er the globally analytic vectors of\nthe pro-p Iwahori group $I$ in the p rincipal series representations. This\nis done by endowing the pro-p Iwah ori with a $p$-valuation and subsequently\ngiving it a structure of a rigi d analytic group\, thus generalizing the work\nof Lazard. The main result of this talk will be the topological\nirreducibility of these globally ana lytic vectors under certain assumptions\non $\\chi$. This is a generalizat ion of works of Clozel and Ray in the case\nof $G:= GL_n(L)$. This is join t work with Claus Sorensen.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Haiyang Wang (University of Georgia) DTSTART:20240312T201500Z DTEND:20240312T211500Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/9 DESCRIPTION:Title: Elliptic curves with potentially good supersing ular reduction and coefficients of the classical modular polynomials\n by Haiyang Wang (University of Georgia) as part of Binghamton Arithmetic S eminar\n\n\nAbstract\nLet $O_K$ be a Henselian discrete valuation domain w ith field of fractions $K$. Assume that $O_K$ has algebraically closed res idue field $k$. Let $E/K$ be an elliptic curve with additive reduction. Th e semi-stable reduction theorem asserts that there exists a minimal extens ion $L/K$ such that the base change $E_L/L$ has semi-stable reduction. It is natural to wonder whether specific properties of the semi-stable reduct ion and of the extension $L/K$ impose restrictions on what types of Kodair a type the special fiber of $E/K$ may have. \n\nIn this talk we will disc uss the restrictions imposed on the reduction type when the extension $L/K $ is wildly ramified of degree 2\, and the curve $E/K$ has potentially goo d supersingular reduction. We will also talk about the possible reduction types of two isogenous elliptic curves with these properties and its relat ion to the congruence properties of the coefficients of the classical modu lar polynomials.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Shane Chern (Dalhousie University) DTSTART:20240319T201500Z DTEND:20240319T211500Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/10 DESCRIPTION:Title: The Seo-Yee conjecture: Nonmodular infinite pr oducts\, seaweed algebras\, and integer partitions\nby Shane Chern (Da lhousie University) as part of Binghamton Arithmetic Seminar\n\n\nAbstract \nIn this talk\, I will present my recent work on the Seo-Yee conjecture\, which claims the nonnegativity of coefficients in the expansion of a q-se ries infinite product. The Seo-Yee conjecture arises from the study of sea weed algebras (a special type of Lie algebra)\, and is closely tied with t he enumeration 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://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Anitha Srinivasan (Universidad Pontificia Comillas\, Madrid) DTSTART:20260317T200000Z DTEND:20260317T210000Z DTSTAMP:20260404T111102Z UID:BinghamtonArithmeticSeminar/11 DESCRIPTION:Title: The generalized Markoff equation\nby Anit ha Srinivasan (Universidad Pontificia Comillas\, Madrid) as part of Bingha mton Arithmetic Seminar\n\n\nAbstract\nThe talk will look at various aspe cts 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 topics that will be mentioned are: the classification of solution tripl es $(a\, b\, c)$ that come from $k$-Fibonacci sequences\, open conjecture s (which $m's$ have no solutions?)\, counting algorithms for the number of solutions (trees) and the Markoff equation mod $p$.\n LOCATION:https://stable.researchseminars.org/talk/BinghamtonArithmeticSemi nar/11/ END:VEVENT END:VCALENDAR