Pattern formation, energy landscapes, and scaling laws

Felix Otto

Contact: Email
+49 (0) 341 - 9959 - 950

Inselstr. 22
04103 Leipzig

Administrative Assistant:
Katja Heid
Email, Phone/Fax:
+49 (0) 341 - 9959
- 951
- 658

Lecture in the Summer term 2023

Bielefeld-Leipzig online seminar: Mathematics of Machine Learning


In this online course we aim to get acquainted with some of the recent progress in the mathematical understanding and theory of machine learning. Particular emphasis will be laid upon overparametrization, implicit bias and aspects of unsupervised learning. The aim of the course is to get an overview of a series of recent articles and the methods developed therein. The course is directed to non experts with a solid background in mathematics aiming to get an idea of recent progress in the mathematics of machine learning. Active contribution in form of a presentation of a research paper (to be chosen) is required for each participant.
During the first five sessions of this course, an introduction to the field of (supervised and un-supervised) machine learning will be given.
To keep informed about changes to this lecture, check Benjamin Gess website regularly. You can obtain the password contacting Benjamin Gess via email

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Blow-up techniques in harmonic measure

  • Lecturer: Max Goering
  • Date: Tuesdays, 09.30-11.00
  • Room: MPI MiS A3 01
  • Keywords: harmonic measure, geometric measure theory, blow-up analysis, free boundary problems
  • Prerequisites: Real analysis, a first course in PDE


The first lecture will briefly cover prerequisites from Mattila's "Geometry of Sets and Measures" including: rectifiability and tangent measures. It will also give an overview of the types of results one could hope for relating the behavior of measures corresponding to a Dirichlet problem and the geometry of the boundary. We will proceed to discuss the two phase harmonic measure free boundary problem, with an initial discussion of the special case of the complex plane. We will then study the blow-up analysis and techniques from Kenig-Toro 2003, Kenig-Toro 2006, and Kenig-Preiss-Toro 2009.

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Other lectures at MPI MIS

Please follow this link for all regular lectures at the Max-Planck-Institute.

06.06.2023, 02:30