Manchester Number Theory Seminar - Kostas Karagiannis
| Dates: | 6 December 2022 |
|---|
| Times: | 15:00 - 16:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
| Who is it for: | University staff, External researchers, Current University students |
|---|
|
Speaker: Kostas Karagiannis (University of Manchester)
Title: The Galois module structure problem for Fermat curves
Abstract: The function field analogy is a general principle that states that the behavior of number fields has striking similarities to that of transcendental extensions of finite fields. The latter arise naturally as function fields of algebraic curves, thus giving a geometric flavor to Galois theory. In this talk, I will discuss how tools from representation theory can be implemented into the context of Galois theory of curves, focusing on automorphism groups of Fermat curves. The need for explicit calculations leads to sums of roots of unity that resemble Kloosterman sums, giving an unexpected connection to analytic number theory. Time permitting, I will discuss how the subject fits into the general framework, by introducing equivariant versions of classic algebro-geometric invariants, such as Euler characteristics and Hilbert functions.
Room: Frank Adams 1
Travel and Contact Information
Find event
Frank Adams 1
Alan Turing Building
Manchester
