Minimal volume entropy is one of many topological invariants of manifolds introduced by Gromov in his seminal article Volume and bounded cohomology of 1982. I will quickly review its definition and its connection with other invariants such as simplicial volume. I will then give an overview on a fundamental rigidity result of Besson, Courtois and Gallot for the minimal volume entropy of closed manifolds admitting locally symmetric metrics of negative sectional curvature, focusing especially on the tools used for its proof in dimension 2.

In the final part I will show how to compute minimal volume entropy for a class of mildly singular spaces and show some attempts at using this computation and the machinery of Besson-Courtois-Gallot to obtain lower estimates, depending on genus and diameter, for the systole of a hyperbolic surface. This is ongoing work with A. Sambusetti and part of my PhD project.

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Questo incontro sarà un'introduzione informale ai seminari dei Baby Geometri. Noi organizzatorə vogliamo presentarci e raccontare la nostra ricerca con dei brevi talk (5 minuti). Ogni domanda è benvenuta, vi aspettiamo!

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