**Problem of the Week**

**BUGCAT**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

**BingAWM**

**Math Club**

seminars:arit

**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

**ORGANIZERS**:

**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):
http://people.math.binghamton.edu/borisov/UpstateNYOnline/Colloquium.html

- ————————- Fall 2023
- Spring 2023 ——– Fall 2022
- Spring 2022 ——– Fall 2021
- Spring 2021 ——– Fall 2020
- Spring 2020 ——– Fall 2019
- Spring 2019 ——– Fall 2018
- Spring 2018 ——– Fall 2017
- Spring 2017 ——– Fall 2016
- Spring 2016 ——– Fall 2015
- Spring 2015 ——– Fall 2014

**January 23**

: N/A*Speaker*

: Organizational Meeting*Title*

: We will discuss plans for this semester*Abstract*

**February 13**

: Alexander Borisov (Binghamton)*Speaker*

: Locally Integer Polynomial Functions*Title*

: 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.*Abstract*

**February 20**

: Sayak Sengupta (Binghamton)*Speaker*

: Nilpotent and Infinitely Nilpotent Integer Sequences*Title*

: 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.*Abstract*

**March 12**by Zoom: Zoom link

: Haiyang Wang (UGA)*Speaker*

: Elliptic curves with potentially good supersingular reduction and coefficients of the classical modular polynomials*Title*

: 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.*Abstract*

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**

: Shane Chern (Dalhousie)*Speaker*

: TBA*Title*

: TBA*Abstract*

**March 26**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

**April 2**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

**April 9**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

**April 16**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

**April 30**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

seminars/arit.txt · Last modified: 2024/02/28 13:07 by borisov

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 3.0 Unported