publication . Preprint . 2021

Trou spectral dans les groupes simples

de Saxcé, Nicolas; He, Weikun;
Open Access French
  • Published: 10 Nov 2021
  • Country: France
Abstract
Nous montrons la propri\'et\'e du trou spectral pour la famille des graphes de Cayley obtenus par r\'eduction modulo $q$ d'un sous-groupe de $\mathrm{SL}_d(\mathbb{Z})$ dont l'adh\'erence de Zariski est un $\mathbb{Q}$-groupe simple. -- We show a spectral gap property for the family of Cayley graphs obtained by reduction modulo $q$ of a subgroup of $\mathrm{SL}_d(\mathbb{Z})$ whose Zariski closure is a simple $\mathbb{Q}$-group.
Comment: in French
Subjects
free text keywords: Mathematics - Group Theory, [MATH]Mathematics [math]
Funded by
EC| HomDyn
Project
HomDyn
Homogenous dynamics, arithmetic and equidistribution
  • Funder: European Commission (EC)
  • Project Code: 833423
  • Funding stream: H2020 | ERC | ERC-ADG
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