Seminario Teoría de grupos 03/03

11:30 Aula Gris 2 ICMAT

Speaker: Geoffrey Janssens (Free University of Brussels)

Title: Which amalgamated products exist in $GL_n(D)$?

Abstract: Given two finite subgroups $G, H in GL_n(D)$, with $D$ a $mathbb{Q}$-division algebra, we will discuss the existence of $G star_{G cap H} H$ inside $GL_n(D)$. The focus of the main part of the talk will be on explaining explicit constructions. In the last part we will turn the attention to the quantity of so called ping-pong partners for a given finite subgroup. More precisely it will turn out that inside $GL_n(mathcal{O})$, for $mathcal{O}$ an order in $D$, they form a profinite dense set. This talk is based on joint (ongoing) work with Doryan Temmerman.


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Seminario Teoría de grupos 10/03
11:30 Aula Naranja ICMAT

Speaker: Matteo Vannacci (University of the Basque Country)

Title: Representations over finite fields, Probability and Zeta Functions

Abstract: In this talk we will study representation growth of a profinite group G over finite fields. On one hand, having "asymptotically few" representations over finite fields connects to (surprising) probabilistic generation properties of the completed group-ring of G. On the other hand, we can encode the number of representations of G over finite fields into a zeta-function and we will investigate how analytic properties of this zeta-function connect to properties of the original group G and its completed group-ring. This is joint work with Ged Corob-Cook and Steffen Kionke.