School of Mathematics

An Euler system for genus 2 Siegel modular forms

David Loeffler
University of Warwick
November 8, 2017

Abstract:  Euler systems are compatible families of cohomology classes for a global Galois represenation, which plan an important role in studying Selmer groups.  I will outline the construction of a new Euler system, for the Galois representation associated to a cohomological cuspidal automorphic representation on the symplectic group GSp(4).  This is joint work with Chris Skinner and Sarah Zerbes. 

A derived Hecke algebra in the context of the mod $p$ Langlands program

Rachel Ollivier
University of British Columbia
November 8, 2017

Abstract: Given a p-adic reductive group G and its (pro-p) Iwahori-Hecke algebra H, we are interested in the link between the category of smooth representations of G and the category of H-modules. When the field of coefficients has characteristic zero this link is well understood by work of Bernstein and Borel.

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.)