Department of Mathematics,
University of California San Diego
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Math 211A: Seminar in Algebra
Dr. Daniele Garzoni
University of Southern California
Characteristic polynomial of random matrices, and random walks
Abstract:
In the talk, we will discuss the irreducibility and the Galois group of random polynomials over the integers. After giving motivation (coming from work of Breuillard--Varju, Eberhard, Ferber--Jain--Sah--Sawhney, and others), I will present a result, conditional on the extended Riemann hypothesis, showing that the characteristic polynomial of certain random tridiagonal matrices is irreducible, with probability tending to 1 as the size of the matrices tends to infinity.
The proof involves random walks in direct products of \({\rm SL}_2(\mathbb{F}_p)\), where we use results of Breuillard--Gamburd and Golsefidy--Srinivas.
Joint work with Lior Bary-Soroker and Sasha Sodin.
Host: Alireza Golsefidy
March 31, 2025
3:00 PM
APM 7321
Research Areas
Algebra****************************
