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"

To how many regions do n hyperplanes divide Rd? This simple question becomes even more interesting if we consider the complement of n hyperplanes in Cd, 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