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, Arithmetic Topology, etc.

PLACE and TIME: This semester the seminar meets primarily on Tuesdays at 4:00 pm, with possible special lectures at other days and times. The in-house talks will be in-person, while visitors outside of Binghamton area will be in-person or by Zoom: Zoom link

ORGANIZERS:
Regular Faculy: Alexander Borisov, Marcin Mazur, Adrian Vasiu.
Post-Docs: Huy Dang

Current Ph.D. students: 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), Patrick Carney (May 2023), Sarah Lamoureux (Sep. 2023), Sayak Sengupta (May 2024).

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 2025
• Spring 2025 ——– Fall 2024
• Spring 2024 ——– 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 27
  Speaker: NA
  Title: Organizational Meeting
  Abstract:
  

• February 3 (2:45-3:45 pm, cross-listed from Algebra Seminar)
  Speaker: Tim Riley (Cornell University)
  Title: Conjugator length
  Abstract: The conjugacy problem for a finitely generated group $G$ asks for an algorithm which, on input a pair of words u and v, declares whether or not they represent conjugate elements of $G$. The conjugator length function $CL$ is its most direct quantification: $CL(n)$ is the minimal $N$ such that if $u$ and $v$ represent conjugate elements of $G$ and the sum of their lengths is at most $n$, then there is a word $w$ of length at most $N$ such that $uw=wv$ in $G$. I will talk about why this function is interesting and how it can behave, and I will highlight some open questions. En route I will talk about results variously with Martin Bridson, Conan Gillis, and Andrew Sale, as well as recent advances by Conan Gillis and Francis Wagner.
  

• February 10
  Speaker: Alexander Borisov (Binghamton)
  Title: A structure sheaf for Kirch topology, an update
  Abstract: TBA
  

• February 17
  Speaker: Mithun Veettil (Binghamton)
  Title: TBA
  Abstract: TBA
  

• February 24
  Speaker: Hari Asokan (Binghamton)
  Title: TBA
  Abstract: TBA
  

• March 3
  Speaker: Connor Stewart (CUNY)
  Title: Conductor–Discriminant Inequality for Tamely Ramified Cyclic Covers
  Abstract: TBA
  

• March 10
  Speaker: Eric Yin (Binghamton)
  Title: TBA
  Abstract: TBA
  

• March 17
  Speaker: Anitha Srinivasan (Comillas University, Madrid), by Zoom
  Title: The generalized Markoff equation
  Abstract: The 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 topics that will be mentioned are: the classification of solution triples $(a, b, c)$ that come from $k$-Fibonacci sequences, open conjectures (which $m's$ have no solutions?), counting algorithms for the number of solutions (trees) and the Markoff equation mod $p$.
  

• March 24
  Speaker: TBA
  Title: TBA
  Abstract: TBA
  

• April 14
  Speaker: TBA
  Title: TBA
  Abstract: TBA
  

• April 21
  Speaker: Joe Kramer-Miller (Lehigh University)
  Title: TBA
  Abstract: TBA
  

• April 28
  Speaker: TBA
  Title: TBA
  Abstract: TBA