525 Malott Hall
Ph.D. (2003) University of Michigan
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.
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.