# Jerusalem Mathematics Colloquium

Thursday, 21 May 1998, 4:00 pm

Mathematics Bldg., lecture hall 2

## Ehud de Shalit (The Hebrew University of Jerusalem)

## "Cutting cheese and the cohomology of p-adic symmetric domains"

** Abstract: **

To how many regions do n hyperplanes divide R^{d}?
This simple question becomes even more interesting if we consider the
complement of n hyperplanes in C^{d}, PROVIDED we rephrase it as:
what is the cohomology ring of such a domain?
We shall review the work of Arnold ('69), Brieskorn ('73) and
Orlik and Solomon ('80), giving a precise
description of the cohomology of the hyperplane complement
in terms of generators and relations.
Recently a connection was discovered between this theory of "complements
of hyperplane arrangements", and the cohomology of the p-adic symmetric
domains introduced in the 70's by Drinfel'd. Rather than one ring, we get
here a local system of rings on the Bruhat-Tits building of PGL(d+1),
each resembling the Orlik-Solomon ring. We shall describe our results, as
well as relations to harmonic analysis on the building, and (if time
permits) to a new theory of higher-dimensional residues.

No previous acquaintance with cohomology OR buildings will be assumed.

Coffee, Cookies at the faculty lounge at 3:30.

List of talks, 1997-98