Tuesday, April 16, 2019 - 15:00
Aula 1B1, Pal. RM002
Incontri di Algebra e Geometria allo SBAI
Filippo Cerocchi (Sapienza Università di Roma)
Acylindrical actions on simplicial trees and their geometric implications
In the first part of the talk we shall survey some classical definition and result of Bass-Serre theory and we shall state some recent result describing features of discrete groups acting acylindrically and without edge inversions on simplicial trees. In the second part we shall present several families of topological spaces whose fundamental groups admit such an action, we shall introduce the entropy of a compact Riemannian manifold and we shall state various results concerning families of Riemannian manifolds with bounded entropy and diameter (systolic estimates, local rigidity results, finiteness results). If time permits we shall also state a precompactness theorem under the extra assumption of non-positive curvature. Based on several works with Andrea Sambusetti (Sapienza, Dipartimento di Matematica).