Back to Departmental Colloquium: Spring 2021
Departmental Colloquium
Date: Thursday, Feb 25, 2021
Time: 4:00PM
Location: JWB 335
Frank Calegari
University of Chicago
Title |
Recent progress in the arithmetic of the Langlands Program |
Abstract |
Choose a random polynomial with integer coefficients, say x^3 + 1 or x^5 + x + 1. If you choose a prime number p, what is the probability that the values of these polynomials will be squares modulo p? Half the time? More than half the time? Less? Some of these elementary questions ultimately lead to difficult problems in the Langlands program. The goal of this colloquium is to show how recent advances in the Langlands program can provide new answers to these questions, and how they are linked to a possible notion of a “Galois group” of systems of polynomial equations in higher dimensions. |
Number Theory