Abstract:  Most finite simple groups have presentations with 2 generators and at most 50 relations.  All alternating and symmetric groups have presentations with 3 generators and 7 relations.  These and similar results (obtained with Guralnick, Kassabov and Lubotzky) are unexpected:  previous presentations for these groups used unbounded numbers of relations. 
I will emphasize the more familiar alternating and symmetric group cases.

Tee/Kaffee/Gebäck
ab 15:30 Uhr
Arnimallee 3, Raum 006