seminars:arit

## 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 on Mondays at 3:30 p.m. or on Tuesdays at 4:15 p.m. in WH 100E, with possible special lectures at other days. Before the talks, there will be refreshments in WH-102.

ORGANIZERS:
Regular Faculy: Alexander Borisov, Marcin Mazur, Adrian Vasiu,
Post-Docs: Vaidehee Thatte.

Current Ph.D. students: Patrick Carney, Andrew Lamoureux, Micah Loverro, and Sayak Sengupta.

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).

Related seminar: The student/postdoc “No Theory Seminar”: https://sites.google.com/view/vaideheethatte/conference-seminar-organization/nts-bu

#### Fall 2019

• August 27 (Tuesday)
Speaker: N/A
Title: Organizational Meeting
Abstract: We will discuss schedule and speakers for this semester
• September 10 (Tuesday)
Speaker: Alexander Borisov (Binghamton University)
Title: Geometrically nilpotent subvarieties for polynomial maps over finite fields
Abstract: For every dominant self-map of an affine space over a finite field, periodic orbits are Zariski dense. In particular, it is not possible that all points over the algebraic closure of the field are sent to one fixed point by some iteration of this polynomial map. However there may exist a proper subvariety of the affine space such that all its points over the algebraic closure are sent to a fixed point by some iteration of the map, yet the variety itself is not. I will give several examples of this phenomenon and discuss some related questions.
• September 17 (Tuesday)
Speaker: Alexander Borisov (Binghamton University)
Title: Lattices in Euclidean Spaces, Part 1
Abstract: This is a first part of a series of two talks on lattices in Euclidean Spaces and their invariants.
• September 24 (Tuesday)
Speaker: Alexander Borisov (Binghamton University)
Title: Lattices in Euclidean Spaces, Part 2
Abstract: This is a continuation of the talk from September 17. We will follow the recent preprint of Bost to prove the Banaszczyk's remarkable “Transference Inequality”.
• October 7 (Monday)
Speaker: Huy Dang (University of Virginia)
Title: The refined Swan conductor and deformation of Artin-Schreier covers
Abstract: An Artin-Schreier curve is a G:=Z/p-branched cover of the projective line over a field of characteristic p>0. A unique aspect of characteristic p is that there exist flat deformations of a wildly ramified cover so that the number of branch points changes but the genus does not. Using refined Swan conductor, we give the necessary and sufficient conditions for the existence of a deformation between given Artin-Schreier curves. As an application, we show that the moduli space of Artin-Schreier covers of fixed genus g is connected when g is sufficiently large.
• October 15 (Tuesday)
Speaker: Inna Sysoeva (Pittsburgh)
Title: Irreducible representations of braid groups
Abstract: In this talk I'm going to discuss the classification of the irreducible representations of Artin braid group $B_n$ on $n$ strings. All irreducible representations of $B_n$ of dimension less or equal to $n-1$ were classified by Ed Formanek in 1996; the irreducible representations of $B_n$ dimension $n$ for $n\geq 9$ were classified by the speaker in 1999, and for $n\leq 8$ they were classified by Formanek, Lee, Vazirani and the speaker in 2003.
I will give the overview of the known results, and I will talk about the work in progress aimed to classify all the irreducible representations of $B_n$ of dimension less or equal than $2n-9$ for $n\geq 10.$
• October 21/22
Speaker: Fikreab Solomon Admasu (Binghamton University)
Title: TBA
Abstract: TBA
• October 29 (Tuesday)
Speaker: Jaiung Jun (SUNY New Palz)
Title: TBA
Abstract: TBA
• November 4/5
Speaker: TBA
Title: TBA
Abstract: TBA
• November 11 (Monday)
Speaker: Andrew Kobin (University of Virginia)
Title: TBA
Abstract: TBA
• November 18/19
Speaker: TBA
Title: TBA
Abstract: TBA
• November 25/26
Speaker: TBA
Title: TBA
Abstract: TBA
• December 2/3
Speaker: TBA
Title: TBA
Abstract: TBA