• Lecturer: Benjamin Gess
• Date: Wednesdays 16:15-17:45
• Room: Live Stream

Abstract

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.
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• 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

Abstract

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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