College of Liberal Arts & Sciences
Mathematics Colloquium
Abstract:
Langlands program, introduced by Robert Langlands, is a set of conjectures that attempt to build bridges between two different areas: Number Theory and Representation Theory (Automorphic forms). The program is also known as a generalization of a well-known theorem called Fermat’s Last Theorem. More precisely, when Wiles proved Fermat’s Last Theorem, he proved (a special form of) the so-called Taniyama-Shimura conjecture and as a corollary he was able to prove Fermat’s Last Theorem. Note that the Taniyama-Shimura conjecture states that every elliptic curve is modular and the Langlands program is a generalization of the Taniyama-Shimura conjecture.
In this colloquium talk, we will briefly go over the following subjects:
(1) Fermat’s Last Theorem
(2) Taniyama-Shimura conjectures
(3) Elliptic curves and modular forms
And then, if time permits, we will briefly explain Langlands program and L-functions with two main conjectures: the local Langlands correspondence and the Langlands functoriality conjecture. This colloquium will be accessible to graduate students in any area (and undergraduate students who are interested in Number theory or Representation theory) at least for the first 40 to 50 minutes.
*Recordings of the Zoom Session will be available a few hours later in this folder (https://uicapture.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=b23b61cc-a48a-4de7-99fc-ae46015b8b6e ). Find the date of the session you want to watch, and click the session title to watch the recording.