Modularity lifting theorems for non-regular symplectic representations

George Boxer
University of Chicago
November 7, 2017

Abstract:  We prove an ordinary modularity lifting theorem for certain non-regular 4-dimensional symplectic representations over totally real fields.  The argument uses both higher Hida theory and the Calegari-Geraghty version of the Taylor-Wiles method.  We also present some applications of these theorems to abelian surfaces.  (Joint work with F. Calegari, T. Gee, and V. Pilloni.) 

Functoriality and algebraic cycles

Kartik Prasanna
University of Michigan
November 6, 2017

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.)