# Julia Gordon

Ph.D. (2003) University of Michigan

### Research Area

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.

### Selected 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.