Discussion of topics for this semester
The aim of this talk is to build every irreducible representations of GL(2,q) on a field with characteristic prime to q. In order to do that, we first study the representations induced by linear characters of the Borel subgroup and then, we extend the (q-1)-dimensional representation of the mirabolic subgroup.
In this seminar, we delve into different analytic approaches to study groups and their actions. Our journey will be guided by the book [1], authored by Cohen and Gelander, which serves as our roadmap. According to the authors, this book is an introductory text to the topic, but it can also be used "as a lightweight book to take for a one month trek in the Nepali Himalayas".
We will mostly focus our attention on amenability, one of the most important properties of analytic group theory. In the last part of the seminar we will introduce property (T). If we have time, we will also look at the Tits alternative.
See the programme for more details.
Main reference:
Let G = GL(V), where V is a finite-dimensional vector space, and recall that any element in G is uniquely determined by its action on a basis for V. In addition, any two pairs of linearly independent vectors can be mapped to each other by an element of G. These two basic linear algebra properties can be interpreted in the language of permutation groups, which leads us naturally to the definitions of base and rank of a permutation group. In this talk, I will present some of my recent results on bases for primitive permutation groups, and I will report on recent progress with C.H. Li and Y.Z. Zhu towards a classification of the rank three groups.
TBA
TBA
Research talks
Bass-Serre theory
Totally disconnected locally compact groups
Mixed Topics
Word Growth in Groups
Bass-Serre Theory and Profinite Analogues
p-Adic analytic pro-p groups
Invariant random subgroups
Probabilistic methods in group theory
Buildings