| Wednesday, 17.04.2024 | |
| Type | seminar in the framework of the PDE Afternoon |
| Time | 15:00 - 15:45 |
| Place | University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, Vienna (map) |
| Room | HS 2, ground floor - how to get there |
| Speaker | (IST Austria) |
| Title | Refined properties of the heat flow: entropy dissipation and geometry of the solutions |
| Abstract | In this talk we present several result which follow from a careful analysis of the heat flow over Rd. Starting from the celebrated Bakry—Émery method, we show constructive stability of Beckner's inequalities for the standard Gaussian measure, in the strongest possible norm. We also investigate stability for the Gaussian logarithmic Sobolev inequality, as a limit point of the family. Being this last inequality critical, its study turns out to be complicated, leaving some points in the theory open. At the same time, the interplay between the heat flow and log-concavity appears as a relevant point in the analysis. Thus, we address this issue, finding both negative and positive results. As a further application, we obtain new estimates in the context of Lipschitz transport maps. |
| Notes | This event takes place in hybrid form (in person and online on Zoom). Slides and additional materials are available on the Moodle service of the University of Vienna. If you want to participate, please write an email to matteo.tommasini@univie.ac.at. Further details are available at this link. |
| Attachment | link |
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