COLUMBIA UNIVERSITY Department of Mathematics   Presents the JOSEPH FELS RITT LECTURES   Richard Taylor Harvard The Local Langlands Conjecture Thursday, April 26 Abstract: The local Langlands conjecture states that there is a natural correspondence between the irreducible representations (usually infinite dimensional) of GL(n,Q_p) and the n-dimensional representations of the absolute Galois group of Q_p. It forms a part of the vast web of conjectures proposed by Langlands in lectures in the late 1960's. In this talk I will describe more precisely the statement of the conjecture and discuss why one might care about it. I will also say a little about formal groups and how they can be used to prove the conjecture. * * * * * Meromorphic Continuation of L-functions Friday, April 27 Abstract:  To various arithmetic objects one can attach L-functions which are holomorphic functions in some right half plane. It is conjectured that these L-functions have holomorphic continuation to the entire complex plane and satisfy a simple functional equation relating values at s and 1-s. It is also widely believed that special values of the L-functions (often at points where the value is not directly defined) reflect deep properties of the underlying arithmetic object. Unfortunately the holomorphic continuation of these L-functions is only known in very few instances. In 1947 Brauer proved meromorphic continuation (and functional equation) of all Artin L-functions. Since then there has been very little progress. In this lecture I will introduce L-functions, try to indicate why one should care about them and explain some recent results that give meromorphic continuation (and functional equation) of some other (moderately general) families of L-functions.     - BARNARD CAMPUS - Lehman Auditorium 202 Altschul Hall  4:30 p.m.   Tea will be served each day at 3:45 p.m. in Room 508 Mathematics Building How to get to the Mathematics Department at Columbia University & Lehman Auditorium, Barnard Campus

<![if !supportEmptyParas]> <![endif]>

Math Department Home

Email your comments by filling out our feedback form. This page was last modified on Monday, 19-Mar-2001.