**SMS scnews item created by James East at Fri 27 Nov 2009 1611**

Type: Seminar

Distribution: World

Expiry: 4 Dec 2009

**Calendar1: 4 Dec 2009 1205-1255**

**CalLoc1: Carslaw 375**

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

### Algebra Seminar

# Computing fundamental domains for congruence subgroups of SL2

### Scott Murray

#### Friday December 4, 12:05--12:55pm, Carslaw 375

###### Abstract

This is joint work with Lisa Carbone and Leigh Cobbs of Rutgers
University.

The Bass-Serre theory of groups acting on trees is vital to the structure
theory of certain infinite groups. In this talk, I consider the action of
SL_{2}(F_{q}((t))) and PGL_{2}(F_{q}((t))) on their Bruhat-Tits graph (or
building). By quotienting out the action of congruence subgroups, we get
a class of graphs called fundamental domains. In addition to their
importance in group theory, this construction is believed to give families
of expander graphs.

Before our work, very few of these graphs had been explicitly constructed.
We used Magma to construct them. These constructions allowed us to make
new conjectures on the structure of these graphs, some of which we have
been able to prove. We also found and corrected some errors in previously
published results.

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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