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We are happy to announce the weekly seminar Topological Data Analysis (TDA) organized by the STRUC­TURES Exploratory Project (EP) Mathematics and Data. The goal of the seminar is to bring together people from various backgrounds who are interested in TDA. The prospective topics will, amongst others, include synergies with Ma­chine Learning (ML). Scientists with a background in computer science or ML are particularly encouraged to participate.

Time & Place: Thursdays 11.15 am to 12.45 am at room 0.200, Mathematikon. The first meeting of the semester will take place on April 27th, exceptionally in the SR Statistik 02.104 of the Mathematikon.

The EP Mathematics and Data provides a platform across the fields of the natural sciences and mathematics to discuss applications and foundations of the topological analysis of data (TDA) and beyond. TDA provides versatile tools to uncover potentially hidden topological structures in data. Researches who use TDA in statistical contexts are regularly surprised by its vast sensitivity to non-local correlations.

Please find the Seminar Announcement here.

Current state-of-the-art ma­chine learning methods impress with their capabilities for prediction, classification, or when solving even complex analytical tasks in the case of large language models. However, these methods often appear as a "black box" from the outside which makes it hard to understand how a result was achieved. In his talk on Interpretable Representations and Neuro-symbolic Methods in Deep Learning on April 19, 2023 (11:00 am), Jan Stühmer will discuss several approaches to interpretability in ma­chine learning. The talk will take place in the DKFZ Lecture Hall, Communication Center, INF 280. Jan Stühmer is junior group leader at the Hei­del­berg Institute for Theo­re­ti­cal Studies and Juniorprofessor at KIT.

For further information, see the talk announcement by the Deutsches Krebsforschungszentrum (DKFZ).

We are delighted to announce the compact course on The gradient flow structure of mean curvature flow by Prof Tim Laux, expert for applied geometric analysis at Uni­ver­si­ty of Bonn, who is currently staying in Hei­del­berg as a guest of STRUCTURES. The courses will take place from Tuesday, April 18 to April 26, 14h-16h, respectively. Please find the abstract attached below:

Title: The gradient flow structure of mean curvature flow
Abstract: Mean curvature flow is the most basic geometric evolution equation for embedded surfaces. Folklore says that it can be viewed as a gradient flow. This course aims at making this statement more precise and harnessing this structure for rigorous analysis. After a brief introduction to the field, I will present some of the ideas behind the (conditional) existence and (weak-strong) uniqueness theory for solutions to mean curvature flow. Focusing on the simple two-phase case, i.e., the evolution of a closed hypersurface, allows for a self-contained and concise presentation, which is accessible for graduate students (master or PhD) with some background in PDEs and functional analysis. The course is structured into four lectures as follows. The first lecture provides an overview, basic examples, and some motivation from numerics and data science. In the second lecture, I'll discuss different weak solution concepts, present a (conditional) closure theorem and relate different solution concepts. The third lecture is devoted to the weak-strong uniqueness principle via a concept of gradient flow calibrations. In the last lecture, I'll show how to use this structure for proving optimal convergence rates for numerical schemes.