Tag - Representation theory

Patrick Allen: Adjoint Selmer groups for polarized automorphic Galois representations

15th October, 2015

Given the p-adic Galois representation associated to a regular algebraic polarized cuspidal automorphic representation, one naturally obtains a pure weight zero representation called its adjoint representation. Because it has weight zero, a conjecture of Bloch and Kato says that the only de Rham extension of the trivial representation by this adjoint representation is the split extension. We will discuss a proof of this case of their conjecture, under an assumption on the residual representation. This is done by using the Taylor-Wiles patching method, Kisin's technique of analyzing the generic fibre of deformation rings, and a characterization of smooth closed points in the generic fibre of certain local deformation rings.

David Hansen: Motivic cohomology actions and the geometry of eigenvarieties

1st October, 2015

Venkatesh has recently proposed a fascinating conjecture relating motivic cohomology with automorphic forms and the cohomology of arithmetic groups. I'll describe this conjecture, and discuss its connections with the local geometry of eigenvarieties and nonabelian analogues of the Leopoldt conjecture. This is joint work with Jack Thorne.

Jacob Lurie: Categorification of the Fourier Transform

24th April, 2015

In this talk, I will discuss the process of 'categorification'; that is, taking a known statement about concrete objects (like sets) and looking for a generalization (or analogue) in a more abstract setting. I will give some specific examples, beginning with the classical theory of the Fourier transform, and (if time permits) briefly discuss how the 'categorification' of this theory arises in geometric representation theory.

Jacob Lurie: Categorification of the Fourier Transform

24th February, 2015

In this talk, I will discuss the process of 'categorification'; that is, taking a known statement about concrete objects (like sets) and looking for a generalization (or analogue) in a more abstract setting. I will give some specific examples, beginning with the classical theory of the Fourier transform, and (if time permits) briefly discuss how the 'categorification' of this theory arises in geometric representation theory.