Synopsis and Organizers

Geometric methods in representation theory and number theory

The Master Lectures by Professor Schmid will center around Lie groups and arithmetic. The Master Lectures themselves will cover the Peter-Weyl theorem, the Weyl character formula, and analogues for noncompact Lie groups. A main theme will be the decomposition of L2(G/H), where H is a subgroup of a reductive Lie group G. In particular interesting nontempered representations occur, and are important in understanding theunitary dual of G -- a topic which several of the workshop lectures will be devoted to. The most important applications are for arithmetic subgroups H; there will also be several lectures on applications of representation theory to automorphic forms, L-functions, and Voronoi summation formulas. In particular the lectures will cover the use of automorphic distributions in analytic number theory, such as in deriving subconvexity estimates for GL(3) L-functions and cancellation in arithmetically twisted sums.


Wilfried SchmidHarvard University
Shouwu ZhangPrinceton University
Dragan MilicicUniversity of Utah
Stephen D. MillerRutgers, The State University of New Jersey
Ye TianChinese Academy Of Sciences
Xinyi YuanPrinceton University