Functoriality and algebraic cycles

Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program
Topic:Functoriality and algebraic cycles
Speaker:Kartik Prasanna
Affiliation:University of Michigan
Date:Monday, November 6
Time/Room:10:00am - 11:00am/S-101
Video Link:https://video.ias.edu/MotivesGaloisRepsandCohomology/2017/1106-KartikPrasanna

Abstract:  I will discuss the following question:  is Langlands functoriality given by algebraic cycles?  After a survey of some examples of interest, the talk will focus mostly on one case, namely that of inner forms GL(2) over a totally real field.  In this case, we can show that functoriality is given by something close to an absolute Hodge cycle; moreover, there is some hope of doing even better. (Joint work with Atsushi Ichino.)