Research Focus
Representation theory of p-adic groups, and motivic integration
My research has been focused on applying a method called motivic integration to harmonic analysis on p-adic groups. Motivic integration is based on model theory, and allows one to do integration on p-adic manifolds in an abstract way, independently of p. I have been contributing to the program initiated by T.C. Hales aiming at restating representation theory of p-adic groups in a p-independent way, using this technique. More recently (with J. Achter and S. Ali Altug), I have been using this abstract approach to measure to help connect different ways of computing the sizes of isogeny classes of abelian varieties. I have also recently become interested in the Trace Formula and its applications.
Publications
- Elliptic curves, random matrices and orbital integrals (with J. Achter and with an appendix by S. Ali Altug), Pacific J. Math., 286 No. 1 (2017), 1-24.
- Appendix B to "Sato-Tate theorem for families and low-lying zeros of automorphic L-functions" by S.-W. Shin and N. Templier (with R. Cluckers and I. Halupczok), in Invent. Math., January 2016, Volume 203, Issue 1, 152-177.
- Local integrability results in harmonic analysis on reductive groups in large positive characteristic (with R. Cluckers and I. Halupczok), Ann. Sci. Ec. Norm. Sup., Volume 47 (2014), No. 6, 1163-1195.
- Motivic functions, integrability, and uniform in p bounds for orbital integrals (with R. Cluckers and I. Halupczok). Electronic Math. Research Announcements in Math. Sciences, volume 21 (2014), 137-152.
