Speaker: Giacomo Micheli
University of South Florida
Will give a Colloquium entitled:
Conspiring primes in Arboreal Galois Representations
Abstract: In this talk we first recall the notion of arboreal Galois representation and then we develop a method to effectively determine the set of primes p for which certain arboreal Galois representations are surjective modulo p. Our method is based on a combination of height bounds on integral points on elliptic curves over function fields in positive characteristic and the ABC theorem for function fields. Using this technique we prove Jones' conjecture [Conjecture 6.7, Compositio Math. 43 (5) (2007)] on the surjectivity of the arboreal Galois representation attached to f=x^2+t. This is a joint work with Andrea Ferraguti.
Date: 10-02-2024
Time: 4:00 pm
Location: 231 Hayes-Healy Bldg