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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:**

**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

- 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

**August 27**

: N/A*Speaker*

: Organizational Meeting*Title*

: We will discuss plans for this semester*Abstract*

**September 3**(Algebra Seminar, cross-listed,**2:50-3:50 pm**)

: Dikran Karagueuzian (Binghamton)*Speaker*

: Elliptic Curves for Dummies*Title*

: A theorem on the random variable of inverse image sizes for a polynomial over a finite field of order q computes the moments of the random variable of inverse images sizes up to an error term. This error term decreases with the inverse of the square root of q. Standard results in the theory of elliptic curves will be used to show that this error term cannot generally be improved. No familiarity with the extensive theory of elliptic curves will be assumed.*Abstract*

**September 10**

: Alexander Borisov (Binghamton)*Speaker*

: A Primer on Modular Forms*Title*

: I will give a very brief introduction to the theory of modular forms. The topics will include the action of the group of invertible 2×2 integer matrices on the upper half plane, the classical fundamental region, the modular functions and forms of even weight, the Eisenstein series. If time permits, I will also talk about Hecke operators, Petersson inner product, and forms of higher level. The main reference for the talk is the last chapter of the classical book by J.-P. Serre “A Course in Arithmetic”.*Abstract*

**September 17**(Unusual time:**4:45-5:45 pm**)

: Noah Stephens-Davidowitz (Cornell)*Speaker*

: A reverse Minkowski theorem*Title*

: Minkowski's celebrated first theorem is one of the foundational results in the study of the geometry of numbers, and it has innumerable applications from number theory to convex geometry to cryptography. It tells us that a lattice (i.e., a linear transformation of Z^n) that is globally dense (i.e., has low determinant) must be locally dense (i.e., must have many short vectors). We will show a proof of a nearly tight converse to Minkowski's theorem, originally conjectured by Daniel Dadush—a lattice with many short points must have a sublattice with small determinant. This “reverse Minkowski theorem” has numerous applications in, e.g., complexity theory, additive combinatorics, cryptography, the study of Brownian motion on flat tori, algorithms for lattice problems, etc. Just recently, it was used by Reis and Rothvoss to give the first asymptotic improvement to integer programming in nearly forty years.*Abstract*

Based on joint work with Oded Regev.

**September 24**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

**October 15**

: Hari Asokan (Binghamton)*Speaker*

: TBA*Title*

: TBA*Abstract*

**October 22**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

**October 29**

:*Speaker*

Jaiung Jun (SUNY New Paltz, IAS): TBA*Title*

: TBA*Abstract*

**November 5**

: Mithun Veettil (Binghamton)*Speaker*

: TBA*Title*

: TBA*Abstract*

**November 12**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

**November 19**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

**December 3**

: TBA*Speaker*

: TBA*Title*

: TBA*Abstract*

seminars/arit.txt · Last modified: 2024/09/11 14:43 by borisov

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