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: 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 $\mathbb{Q}_p((t))$.