3 dec 2024 -- 14:30
Aula Riunioni, Dipartimento di Matematica, Pisa
Abstract.
I will present two rigidity results about CAT(0)-spaces. The first one concerns the isolation of flat spaces among (geodesically complete) CAT(0)-spaces admitting cocompact lattices, provided that the codiameter is uniformily bounded. The second one is an entropy-pinching theorem saying that if a uniformly packed and uniformly cocompact CAT(0)-space has entropy small enough, then it is flat. Both results stem from a careful study of the theory of (equivariant) Gromov-Hausdorff convergence of lattices of CAT(0)-spaces and of their possible degenerations, whose main lines I will try to explain.