Motivic Integration, Orbital Integrals, and Zeta-Functions (14w5155)

Arriving Sunday, November 30 and departing Friday December 5, 2014

Organizers

William Casselman (University of British Columbia)
Julia Gordon (University of British Columbia)
Francois Loeser (Institut Mathematique de Juisseu)

Objectives

The proposed workshop is intended to bring together two distinct mathematical groups -- those working in harmonic analysis on p-adic groups, and those in motivic integraction. The overall objective of the workshop is to understand p-adic orbital integrals better.

The first specific goal is to enable the members of one group to understand the techniques of the other. The second goal is to make the two communities aware of each other's open problems, especially the problems amenable to motivic integration techniques. We hope that some of the problems would in fact be solved during the conference.

The third, less precise goal, is to explore the connection between orbital integrals, arc spaces, and (motivic) Igusa zeta-functions.

The final goal is to produce concrete output in the form of lecture notes. We shall start with a series of introductory talks on (a) motivic integrals, (b) Igusa zeta-functions, (c) arc spaces, vanishing cycles, and Bernstein polynomials.
As stated above, we would like to make sure that there are several introductory talks, in order to facilitate discussions between the two communities. Here are the suggested topics. Please e-mail the organizres if you would like to give one of these introductory talks. It is possible for one participant to give more than one talk, and these talks can be requested to be up to two hours. We will update the website as the speakrs get matched to the topics.


List of possible introductory topics (and possible speakers)

- Real groups, semi-algebraic sets, variations on a theme of Mathieu (W. Casselman).
- Nash manifolds.
- Hrushovski-Kazhdan theory of motivic integration.
- Igusa integrals, Bernstein polynomials, D-modules.
- Vanishing cycles, (motivic) Milnor fibre.
- Orbital integrals.
- A relationship between orbital integrals and Igusa zeta-integrals.