In connection with the annual general meeting (generalforsamling) in the Danish Mathematical Society on March 26, we are having a colloquium style lecture by Fabrice Baudoin (professor in Aarhus and the recipient of both an ERC Advanced grant and a Villum Investigator grant ), which I thought could be of interest to some of you.
Title: Analysis Without Smoothness: Laplacians and Heat Flow on Fractals
Abstract: Fractals are geometric objects with intricate structure at every scale. Although they are easy to conceptualize, they are difficult to study analytically because they are non-smooth spaces: there are no tangent planes and no obvious notion of derivatives.
Nevertheless, one can still develop key tools of analysis on fractals. In this talk I will explain how we construct analogues of the Laplacian and the heat equation on certain fractal sets. The main idea is to approximate the fractal by finite graphs, define energies and Laplacians on these discrete objects, and then pass to a limit. This approach leads to a notion of diffusion on fractals and naturally gives rise to Brownian motion adapted to their geometry. The resulting processes behave in ways that are strikingly different from diffusion in ordinary Euclidean space. The goal of the talk is to give a conceptual overview of how analysis can be developed even in the absence of smooth structure.
Title: Analysis Without Smoothness: Laplacians and Heat Flow on Fractals
Abstract: Fractals are geometric objects with intricate structure at every scale. Although they are easy to conceptualize, they are difficult to study analytically because they are non-smooth spaces: there are no tangent planes and no obvious notion of derivatives.
Nevertheless, one can still develop key tools of analysis on fractals. In this talk I will explain how we construct analogues of the Laplacian and the heat equation on certain fractal sets. The main idea is to approximate the fractal by finite graphs, define energies and Laplacians on these discrete objects, and then pass to a limit. This approach leads to a notion of diffusion on fractals and naturally gives rise to Brownian motion adapted to their geometry. The resulting processes behave in ways that are strikingly different from diffusion in ordinary Euclidean space. The goal of the talk is to give a conceptual overview of how analysis can be developed even in the absence of smooth structure.
- Organizer: IMADA
- Address: Campusvej 55, 5230 Odense M
- Contact Email: dkyed@imada.sdu.dk
- The talk takes place in U49A: https://clients.mapsindoors.com/sdu/573f26e4bc1f571b08094312/details/563cb8e9423b7d0540c9a2b6
- Add to your calendar: https://eom.sdu.dk:443/events/ical/b30f2a34-0a85-4a80-a9c5-b1c41272cdbd