**SMS scnews item created by James East at Mon 29 Jun 2009 1025**

Type: Seminar

Distribution: World

Expiry: 3 Jul 2009

**Calendar1: 3 Jul 2009 1205-1255**

**CalLoc1: Carslaw 375**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

# Existence, covolumes and infinite generation of lattices for Davis complexes

### Anne Thomas

#### Friday July 3, 12:05--12:55pm, Carslaw 375

###### Abstract

Let Sigma be the Davis complex for a Coxeter system (W,S). The automorphism group G of Sigma is naturally a locally compact group, and a simple combinatorial condition due to Haglund-Paulin determines when G is nondiscrete. The Coxeter group W may be regarded as a uniform lattice in G. We show that many such G also admit a uniform lattice Gamma, and an infinite family of nonuniform lattices with covolumes converging to that of Gamma. We also show that the nonuniform lattice Gamma is not finitely generated.

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After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East jamese@maths.usyd.edu.au