Mathematics

Prof. Luis Lomeli
Pontificia Universidad Catolica De Valparaiso

Langlands' functoriality conjectures encompass a vast generalization of classical reciprocity laws that provide crossroads between Number Theory and Representation Theory. We will present an overview and recall the known results for GL(N). Then we will go through the functorial lift for globally generic representations over function fields, specialized to the classical groups. Our main application is a proof of the Ramanujan conjecture for the classical groups in positive characteristic. Time permitting, we will talk about different directions in the Langlands Program.