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Thursday, 24th October 2002, 4:00 pm

Mathematics Building, Lecture Hall 2

Gil Alon

(Hebrew University)

"*p*-adic Hyperplane Arrangements and Buildings of
*GL_n(Q_p)*"

** Abstract: **
Into how many pieces is *R^n* cut, by *n* hyperplanes in
general position in *R^n*? Generalizing the answer to
this question, one defines for any set of hyperplanes in a vector
space, an invariant called the **Orlik-Solomon algebra**.

When the base field is the *p*-adic numbers *Q_p*, there is
another factor in the game: the Bruhat-Tits building of the general
linear group over *Q_p*. It is a highly symmetric simplicial
complex on which the group acts. E. De Shalit attached to a
collection of hyperplanes in a *p*-adic vecor space a certain local
system of algebras, which are local versions of the Orlik-Solomon
algebra. We will define the above notions, calculate the cohomology
of the above system (for a finite number of hyperplanes), and show a
recent combinatorial application.

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

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