## Oussama Hamza [1]

Poincaré Series and mild groups

Thursday, 10 June, 2021 - 15:30 to 16:30

Résumé :

Let $G$ be a pro-$p$-group, which admits a minimal presentation, with $d$ generators and $r$ relations. In $1964$, Golod and Shafarevich showed that if $G$ is a $p$-group, then it satisfies $d^2<4r$. The original proof of this result use a very subtle study of Poincaré Series. Poincaré Series gives also cohomological information on pro-$p$-groups. During the 60's, Lazard and Koch showed that a pro-$p$-group has cohomological dimension less than two if and only if its PoincarÃ© Series verifies some equality. Between 1980 and 2000's, Anick and Labute, introduced a sufficient and easy condition on the relations of pro-$p$-group $G$, such that $G$ is of cohomological dimension less than two. Groups satisfying this sufficient condition are called mild. In this talk, we will present, more precisely, Poincaré series, cohomological consequences, and mild groups. If time permits, we will give some examples in an arithmetic context.

Institution de l'orateur :

Western University (Ontario)

Thème de recherche :

Compréhensible

Salle :

Salle 4/Zoom : https://univ-grenoble-alpes-fr.zoom.us/j/94606276264?pwd=Y2ZGZ2YwMW91SzJVTXpKOG5aRFhDdz09