Seminari di Sistemi Dinamici Olomorfi 2017-2018
timetable:
Wed 2 May, 16:00 - 17:00, Sala Conferenze Centro De Giorgi
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seminar: Potentials, energies and Hausdorff dimension
speaker: Tomas Persson (Lunds Universitet)abstract: There is a classical connection between Riesz-potentials, Riesz-energies and Hausdorff dimension. Otto Frostman (Lund) proved in his 1935 thesis that if E is a set and μ is a measure with support in E, then the Hausdorff dimension of E is at least s if the s-dimensional Riesz-energy of μ is finite. I will first recall Frostman's result and some of its applications. I will then mention some new methods where Hausdorff dimension is calculated using potentials and energies with inhomogeneous kernels. Some applications are in stochastic geometry and dynamical systems. For instance, the method can be used to analyse the Hausdorff dimension of the set of points around which an orbit enters a shrinking target infinitely often.
timetable:
Wed 2 May, 16:00 - 17:00, Sala Conferenze Centro De Giorgi
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