The research of this Presidential Young Investigator concerns the theory of automorphic forms and the applications of the Selberg trace formula. More specifically he will work on the cohomology of arithmetic groups where he will work on his conjecture that non-trivial cohomology always occurs in a certain "main dimension". He also hopes to use cohomology to prove new cases of Langlands functoriality. In addition he will study base change and orbital integrals. This leads to results on the Hasse-Weil zeta functions for some Shimura varieties. Finally he will work on rationality properties of Hecke eigenvalues and special values of L-functions. This research is some of the most important in the very current area of the so called Langlands program. This program combines modern analysis, algebraic geometry and algebra to solve some of the deepest problems in number theory. It has also been very influential through out mathematics. The mastery of all the theory that goes into the work is difficult enough, and Clozel has manipulated these machines in a very effective way in the past. His current program is among the very most promising in all of number theory.
