##### Department of Mathematics,

University of California San Diego

****************************

### Algebra Seminar

## Jamshid Derakhshan

#### Oxford University

## Zeta functions of groups, motivic integrals, and model theory

##### Abstract:

I will present joint work with Mark Berman, Uri Onn, and Pirita Paajanen showing that given a Chevalley group, for large p, the number of conjugacy classes of all the congruence quotients of the group of rational points over the valuation ring of a non-archimedean local field of residue characteristic p depends only on the cardinality of the residue field and not on the ring. This reduces to proving that the conjugacy class zeta function is motivic in the sense that it is given uniformly (across all local fields) by a formula of the model-theoretic language of Denef-Pas-Loeser for valued fields, and then to use a so-called motivic transfer principle. I will then discuss an analogue of this question for the case of a global field and related issues in algebra and number theory. Finally, I will discuss a related general perspective involving a model theory for adeles of a number field and a model theory for finite fields (joint works with Angus Macintyre).

Host: Alireza Salehi Golsefidy

### May 19, 2014

### 2:00 PM

### AP&M 7218

****************************