Talk

We discuss rank one and higher rank superrigidity for the isometry groups of a class of complexes which includes hyperbolic buildings as a special case. Our method uses harmonic maps to singular spaces.

Whittaker functions are special functions on reductive groups, which are naturally arising in the theory of automorphic representations. The talk is devoted to recent results (joint with A. Gerasimov and D. Lebedev) on explicit construction of $q$-deformation of Whittaker functions for the group $GL(N,\mathbb{R})$. In the first part of my talk I will introduce two (integral) representations of $GL(N)$-Whittaker function, using two different limits of Macdonald polynomials. The first representation is a $q$-deformation of the classical Gelfand-Zetlin formula for the character. The other representation provides an identification of the constructed $q$-deformed Whittaker function with a character of certain Demazure module of the corresponding affine Lie algebra $\hat{\eufm gl}(N)$.

This talk will be an introduction to pure motives and to the generalized Birch and Swinnerton-Dyer conjecture relating the order of vanishing of an L-function at the center of the critical strip to the rank of a Chow group. The purpose of the talk is to give general information about the field. No new results will be presented. In keeping with the spirit of the seminar the examples will be taken from motives coming from threefolds whose cohomology has Hodge numbers $h^{30}=h^{21}=h^{12}=h^{03}=1$.

This is the last of the three program discussion. This time we fix the schedule for Thursday and Friday.