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The Arithmetic Seminar

TOPICS: Arithmetic in the broadest sense that includes Number Theory (Elementary Arithmetic, Algebraic, Analytic, Combinatorial, etc.), Algebraic Geometry, Representation Theory, Lie Groups and Lie Algebras, Diophantine Geometry, Geometry of Numbers, Tropical Geometry, Arithmetic Dynamics, etc.

PLACE and TIME: This semester the seminar meets primarily on Tuesdays at 4:15 p.m, with possible special lectures on Mondays at 3:30 or other days and times. The in-house talks will be in-person, while visitors outside of Binghamton area will be by Zoom: Zoom link

Regular Faculy: Alexander Borisov, Marcin Mazur, Adrian Vasiu,
Post-Docs: Sailun Zhan.

Current Ph.D. students: Andrew Lamoureux, Micah Loverro, Sayak Sengupta, Hari Asokan, Mithun Padinhare Veettil.

Graduated Ph.D. students (in number theory and related topics): Ilir Snopce (Dec. 2009), Xiao Xiao (May 2011), Jinghao Li (May 2015), Ding Ding (Dec. 2015), Patrick Milano (May 2018), Changwei Zhou (May 2019).

SEMINAR ANNOUNCEMENTS: To receive announcements of seminar talks by email, please join our mailing list.

Related seminar: Upstate New York Online Number Theory Colloquium (online, irregular):

Previous Arithmetic Seminar Talks

Spring 2024

  • January 23
    Speaker: N/A
    Title: Organizational Meeting
    Abstract: We will discuss plans for this semester
  • February 13
    Speaker: Alexander Borisov (Binghamton)
    Title: Locally Integer Polynomial Functions
    Abstract: I will discuss the ring of integer-valued functions on the integers with a peculiar property: when restricted to any finite subset, the interpolation polynomial has integer coefficients. The original motivation for this comes from Sayak Sengupta's work on iterations of integer polynomials, but this and related objects appear to be of independent interest.
  • February 20
    Speaker: Sayak Sengupta (Binghamton)
    Title: Nilpotent and Infinitely Nilpotent Integer Sequences
    Abstract: We say that an integer sequence $\{r_n\}_{n\ge 0}$ has a generating polynomial $u(x)$ over $\mathbb{Z}$ if for every positive integer $n$ one has $u^{(n)}(r_0)=r_n$. In addition, if such a sequence satisfies the condition that $r_n=0$ for some positive integer $n$ (respectively, $r_n=0$ for infinitely many positive integers $n$), then we say that $\{r_n\}_{n\ge 0}$ is a nilpotent sequence (respectively, $\{r_n\}_{n\ge 0}$ is an infinitely nilpotent sequence). In this talk we will provide (and discuss) some important characteristics of nilpotent and infinitely nilpotent sequences.
  • March 12 by Zoom: Zoom link
    Speaker: Haiyang Wang (UGA)
    Title: Elliptic curves with potentially good supersingular reduction and coefficients of the classical modular polynomials
    Abstract: Let $O_K$ be a Henselian discrete valuation domain with field of fractions $K$. Assume that $O_K$ has algebraically closed residue field $k$. 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 natural 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.
    In this talk we will discuss 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 good supersingular reduction. We will also talk about the possible reduction types of two isogenous elliptic curves with these properties and its relation to the congruence properties of the coefficients of the classical modular polynomials.
  • March 19
    Speaker: Shane Chern (Dalhousie)
    Title: TBA
    Abstract: TBA
  • March 26
    Speaker: TBA
    Title: TBA
    Abstract: TBA
  • April 2
    Speaker: TBA
    Title: TBA
    Abstract: TBA
  • April 9
    Speaker: TBA
    Title: TBA
    Abstract: TBA
  • April 16
    Speaker: TBA
    Title: TBA
    Abstract: TBA
  • April 30
    Speaker: TBA
    Title: TBA
    Abstract: TBA
seminars/arit.txt · Last modified: 2024/02/28 13:07 by borisov