Jamshid Derakhshan
(University of Oxford)
Model Theory, Zeta Functions of Groups, Adeles of Number Fields, and Counting in p-Adic and Finite Fields

I will first present joint work with Mark Berman, Pirita Paajanen, and Uri Onn on the number of conjugacy classes in congruence quotients of algebraic groups over local fields, and applications of motivic transfer principles to this setting. I will then present joint works with Angus Macintyre on model theory for adeles and model theory for counting numbers of points modulo p on algebraic varieties for large p in relation to some work of Serre.

I will finally present a unified point of view on these, formulated in terms of enrichments of the adeles, which also introduces new issues and questions on Archimedean fields.

The talk will be for a general audience.