Past Kinderseminar

16 June 2010
11:30
Jason Semeraro
Abstract

Not only does the definition of an (abstract) saturated fusion system provide us with an interesting way to think about finite groups, it also permits the construction of exotic examples, i.e. objects that are non-realisable by any finite group. After recalling the relevant definitions of fusion systems and saturation, we construct an exotic fusion system at the prime 3 as the fusion system of the completion of a tree of finite groups. We then sketch a proof that it is indeed exotic by appealing to The Classification of Finite Simple Groups.

12 May 2010
11:30
Elisabeth Fink
Abstract
I'll start with the definition of the first Grigorchuk group as an automorphism group on a binary tree. After that I give a short overview about what growth means, and what kinds of growth we know. On this occasion I will mention a few groups that have each kind of growth and also outline what the 'Gap Problem' was. Having explained this I will prove - or depending on the time sketch - why this Grigorchuk group has intermediate growth. Depending on the time I will maybe also mention one or two open problems concerning growth.
10 March 2010
11:30
Peter Neumann
Abstract
The first part of Galois' Second Mémoire, less than three pages of manuscript written in 1830, is devoted to an amazing insight, far ahead of its time. Translated into modern mathematical language (and out of French), it is the theorem that a primitive soluble finite permutation group has prime-power degree. This, and Galois' ideas, and counterexamples to some of them, will be my theme.

Pages