Asymptotic invariants of locally symmetric spaces – Tsachik Gelander – ICM2018

Lie Theory and Generalizations
Invited Lecture 7.4
Asymptotic invariants of locally symmetric spaces
Tsachik Gelander

Abstract: The complexity of a locally symmetric space M is controlled by its volume. This phenomena can be measured by studying the growth of topological, geometric, algebraic, arithmetic and representation theoretic invariants. The most studied invariants are the Betti numbers. Other, and typically less accessible, invariants are: the torsion in homology, the minimal number of generators (and relations) of Γ = π₁(M), the injectivity radius at a random point of M, the possible number of manifolds M of a certain type and bounded volume, the Plancherel measure associated to L2(G/Γ). In the talk I will consider these and other invariants, give upper and lower bounds and focus on the asymptotic behavior.

ICM 2018 – International Congress of Mathematicians ©
 
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