Mathematics Department Colloquium
Spring 2005

Date: Thursday, January 27
Time: 4:00 p.m.
Location: 215 Thomas Building
Name: David Kazhdan
Affiliation: The Hebrew University of Jerusalem
Title: Integration over non-archimedian fields

Abstract: kazhdan-abstract Let $ \psi :\mathbb{Q}_p\to {\mathbb{C}}$ be a non-trivial additive character. Given a polynomial $ f:F^n\to F$ we can define the Fourier transform $ \mathcal F(\psi (f))$ of the function $ \psi (f)$ as a distribution on $ F^n$.

In the first part of the talk I'll explain how to see that the existence of a proper algebraic subset $ X\subset F^n$ such that the restriction of $ \mathcal F(\psi (f))$ is given by a locally constant function.

If time allows I'll try to explain how to define the notion of integration over non-locally compact fields such as $ \mathbb{Q}_p((t))$.