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 SL2(Fq((t))) and PGL2(Fq((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


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