Fall 2026
The seminar typically runs on Fridays from 2:30-4:30 in LC 315. For more information, contact Alex Duncan.
| Date | Location | Speaker | Title | Host |
| Friday, Sep 4 2:30PM |
LC 315 | Frank Thorne University of South Carolina |
Meet-and-Greet / The Jacobian Conjecture | local |
| Friday, Sep 18 2:30PM |
LC 315 | Om Prakash Charles University, Prague / USC |
Classification of universal forms over number fields | Frank Thorne |
Abstracts
Frank Thorne - Meet-and-Greet / The Jacobian Conjecture
We will begin with a short meet-and-greet, so everyone interested in algebra, geometry, and number theory can meet each other. We will also announce AGNT conferences of potential interest happening in the fall. Then, I will give a short talk about the Jacobian Conjecture, a long-standing conjecture in algebraic geometry that was recently disproved by Levent Alpoge and Claude. I'll follow Terry Tao's blog post on this topic, which describes the counterexample in reasonably elementary terms.
Om Prakash - Classification of universal forms over number fields
A universal quadratic form is a positive definite quadratic form with integral coefficients that represents all positive integers--a classical example being the sum of four squares $x^2+y^2+z^2+w^2$. The 290-Theorem of Bhargava and Hanke characterizes positive definite quadratic forms over rational integers are universal as exactly the forms that represent $1,2,3,\dots,290$. In this talk, I will discuss universality of higher degree forms (i.e., homogeneous polynomials of degree $m>2$) over totally real number fields. In particular, I will address the question whether they can be classified by a variant of the 290-Theorem. This is based on a joint work with Vítězslav Kala.