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La mattina del 4 maggio si terrà una mezza giornata di seminari di Analisi Geometrica al Dipartimento di Matematica e Applicazioni dell'Università di Milano Bicocca, presso l'aula 3014 - Edificio U5 coi seguenti oratori:
9:15 - 10:10. Baptiste Devyver (Université de Grenoble): Gradient heat kernel estimates and applications to Sobolev spaces in fractal contexts
Abstract: Estimates of the heat kernel have numerous applications in (geometric) analysis. Obtaining these usually requires to impose some bounds on the Ricci curvature. In this talk, we will consider a setting in which such bounds on curvature are not available, namely cable systems (quatum graphs) with fractal-like structure. Time allowing, we will present some applications related to the definition of Sobolev spaces. This talk is based on joint works with E. Russ (Grenoble) and (partly) M. Yang (Bonn).
10:45 - 11:40. Elia Bruè (Università Bocconi): The fundamental group of manifolds with nonnegative Ricci curvature
Abstract: Estimates of the heat kernel have numerous applications in (geometric) analysis. Obtaining these usually requires to impose some bounds on the Ricci curvature. In this talk, we will consider a setting in which such bounds on curvature are not available, namely cable systems (quatum graphs) with fractal-like structure. Time allowing, we will present some applications related to the definition of Sobolev spaces. This talk is based on joint works with E. Russ (Grenoble) and (partly) M. Yang (Bonn).
11:45 - 12:40. Giulio Colombo (Università Statale di Milano): Tachibana-type theorems on complete manifolds
Abstract: A classical theorem of S.-I. Tachibana states that a closed, orientable Riemannian manifold of dimension m ≥ 3 with harmonic curvature tensor and positive curvature operator is a space of constant curvature. In this talk we show that the same conclusion holds assuming only that the sum of the [(m-1)/2] lowest eigenvalues of the curvature operator is positive, with [ · ] denoting the integer part. This weakened positivity condition originates from recent work of P. Petersen and M. Wink, who proved an analogous result for Einstein manifolds. We also discuss some extensions to the case of complete (and not a priori compact) manifolds.
This is based on a joint work with M. Mariani and M. Rigoli.
Tutti gli interessati sono invitati a partecipare!
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