Colloquium: Tuesday Dec. 24, 2024. Speaker: Lior Bary-Soroker (Tel Aviv). Title: “Probabilistic Aspects of Galois Theory”.
Place: Room 614, Education and Sciences Building, University of Haifa
Zoom link: https://us02web.zoom.us/j/87282501214?pwd=gnoO4TOG9LKBQJrfQ89Od7nUkoy0S3.1
Meeting ID: 872 8250 1214
Abstract: Probabilistic Galois theory explores the arithmetic properties of random polynomials with integer coefficients, focusing on questions such as irreducibility and the structure of their Galois groups. Several natural models of randomness have been studied: the large box model, where the degree is fixed and the coefficients are chosen uniformly from a box of growing size; the large degree model, where the coefficients are independent and identically distributed (e.g., taking values 0 or 1 with equal probabilities) as the degree grows; and models inspired by discrete random matrix theory.
In recent years, there have been significant breakthroughs in understanding the behavior of polynomials under each of these models. This talk will provide an overview of these developments, highlighting the exciting interplay between probability, algebra, and number theory.
