math.html

Julia Gordon: research interests.

math.html I got my Ph.D. from the University of Michigan in 2003. My current research interests are in Representation theory of p-adic groups and motivic integration.

Advisor:

Thomas C. Hales

Papers and Preprints

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 ).
Submitted. In the appendix, we prove a uniform in p bound for normalized orbital integrals.
Definability results for invariant distributions on a reductive unramified p-adic group. (with R. Cluckers and I. Halupczok ).
Under revision, to include ramified groups as well.
Transfer principles for integrability and boundedness conditions for motivic exponential functions (with R. Cluckers and I. Halupczok ).
Submitted.
Transfer to characteristic zero -- appendix to "The fundamental lemma of Jacquet-Rallis in positive characteristics" by Zhiwei Yun.
Duke Math J. 156 No. 2 (2011), 220-227.
On the computability of some positive-depth characters near the identity (with R. Cluckers , C. Cunningham , and L. Spice ).
Represent. Theory 15 (2011), 531-567.
An overview of arithmetic motivic integration. (with Y. Yaffe)
in "Ottawa Lectures on p-adic Groups", C. Cunnigham and M. Nevins, Eds., Fields Institute Monograph Series, 2009.
Motivic proof of a character formula for SL(2) (with Clifton Cunningham ).
Experiment. Math. 18 No.1 (2009), pp.11-44.
Motivic Haar Measure on Reductive Groups .
Canadian J. Math. 58 (2006), No. 1, 93--114.
Motivic nature of character values of depth-zero representations.
IMRN 2004, no. 34, 1735 - 1760.
Virtual Transfer Factors , (with T.C. Hales ).
Represent. Theory 7 (2003), 81--100 (electronic).
Common hypercyclic vector for the multiples of backward shift , (with E.V. Abakumov).
J. Funct. Anal. 200 (2003), no. 2, 494--504.
Composition operators on the space of Dirichlet series with square summable coefficients, (with Haakan Hedenmalm ).
Michigan Math. Journal, 46 (1999), no. 2, 313--329.

Motivic integration in representation theory

Here are some older papers by my advisor and others showing that various constructions arising in representation theory of p-adic groups can be expressed geometrically (for almost all p) by means of motivic integration. The most spectacular application of this approach so far is the transfer priciple for the Fundamental Lemma.

T.C. Hales, Can p-adic integrals be computed? (this is a good place to start).
R. Cluckers, T. Hales, and F. Loeser, Transfer Principle for the Fundamental Lemma .
T.C. Hales, Orbital integrals are motivic.
C. Cunningham and T.C. Hales, Good orbital integrals .
J. Diwadkar Nilpotent conjugacy classes in p-adic Lie algebras: the odd orthogonal case .

Motivic Integration links and resources

2004 complete motivic Integration bibiography , at Manuel Blickle's old page.
Other materials at Manuel Blickle's page.

Raf Cluckers
Wim Veys
Introduction to motivic integration by W. Veys
"What is Motivic Measure?" By T.C. Hales
More resources can be found at an old page for the seminar on motivic integration we had in 2004 at Toronto.

Representation Theory links and resources

David Ben-Zvi's Geometric Langlands page.
Representations of reductive p-adic groups (by Fiona Murnaghan).
A course on representation theory (D. Barbasch)
Collected works of Robert Langlands