Vorträge in der Woche 16.12.2019 bis 22.12.2019

Dienstag, 17.12.2019: Towards topology in neuroscience

Paul Hege (Universität Tübingen)

Topological data analysis is a recently developed method that can be used to compute homology groups of noisy data with improved reliability. In this talk, I will present my own attempts to apply persistent homology to neuroscientific MEG data in the lab of professor Siegel during the last months. As a first step towards possibly finding interesting new structures based on topological information, both connectivity matrices and time series of time-frequency power are shown to contain some subject-specific homology.

Dienstag, 17.12.2019: Representation theory of PGL_2, spectral decomposition of L^2(G(Q)\G(A)) II

Julien Sessler

Donnerstag, 19.12.2019: A sharp logarithmic Sobolev inequality for submanifolds in Euclidean space

Prof. Dr. Simon Brendle (Columbia University)

The logarithmic Sobolev inequality in Euclidean space plays an important role in PDE theory, as well as in probability. In 2000, Klaus Ecker proved a version of the logarithmic Sobolev inequality which holds on any submanifold of Euclidean space, albeit with a non-sharp constant. In this lecture, I will discuss a new approach based on the ABP maximum principle which gives the sharp constant in this inequality. Like the Michael-Simon Sobolev inequality, this inequality contains a term involving the mean curvature (in this case, the shrinker mean curvature).