Motivic integration and motivic Haar measure, zeta functions, and p-adic groups with the Howe - Moore property.

In this research project, we study applications of p-adic and motivic integration to number theory, group theory and algebraic geometry. The main goals are the following:developing a theory of motivic integration with characters, with applications to p-adic representations and the Langlands program,applying motivic integration of Haar measures to the study of arithmetic properties of semi-abelian varieties,studying p-adic and motivic zeta functions associated to equivalence relations on group-theoretic objects,classification of p-adic algebraic groups with the Howe-Moore property. The project will be carried out in collaboration with Prof. F. Loeser (Ecole Normale Supérieure de Paris), Prof. J. Gordon (University of British Columbia), Prof M. du Sautoy (University of Oxford) and Prof. A. Valette (Université de Neuchâtel).

Keywords:P-adic groups, Zeta functions, Abelian varieties, Langlands program, Motivic integration

Disciplines:Algebra, History and foundations