Event Details

A joint event between the pure mathematics seminar series and Open Problems in Mathematics, intended to be accessible to undergraduate students but of interest to postgraduates and academics.

Title: From Factoring mod p to Langlands in 60 minutes!

Abstract: The Langlands program is an (in)famous web of ideas, results and conjectures relating many different areas of mathematics (e.g. representation theory, number theory, algebraic geometry, harmonic analysis, etc). It is often referred to as the holy grail of algebraic number theory, since it unlocks a deep understanding of many mysterious arithmetic phenomena and gives significant insights towards a wide range of open problems in number theory. For example, most of Wiles’ groundbreaking proof of Fermat’s Last Theorem concerns the proof of a “tiny” piece of these conjectures!

In this talk, I will not explain what the Langlands program is since this is very complicated (although I’d be happy to give a second talk on this if desired!). Instead, I want to give an idea of the kind of thing that it aims to do…motivated by the simple sounding problem of factoring polynomials mod p. Examples will be provided!