• Lecturer: Tobias Ried, Florentin Münch, Dejan Gajic, Stefan Czimek
• Date: Mondays 10.30-12.00 (please note special dates and rooms at the lectures)
• Room: MPI MiS E1 05 (Leibniz)
• Audience: IMPRS students and others

Abstract

Due to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field.

Part I: Tobias Ried: Multimarginal Optimal Transport and Applications
Multimarginal optimal transport is a natural generalisation of the classical optimal transport problem. Recently, it received quite some attention due to its applications in density functional theory and statistical learning. In the four lectures I want to introduce the problem, sketch the main existence results and structural properties of optimisers, and highlight some of the applications. The focus will be more on conceptual questions instead of full proofs, and making connections to the many areas of mathematics and applications that multimarginal optimal transport appears in.
Dates: 24.10., 1.11. (Tuesday due to Public holiday!), 7.11. (in G3 10), 14.11

Part II: Florentin Münch: Discrete Ricci Curvature
The lecture aims to give an overview about discrete Ricci curvature notions, particularly, Forman, Ollivier, Bakry Emery, and entropic curvature. We will use a unified approach to the four curvature notions using the Bochner formula and gradient estimates for the heat equation. The main goal is to give a good intuition about the curvature, and to this end, we will calculate the curvature of many examples, and particularly, your favorite graphs.
Dates: 21.11., 28.11. (in G3 10), 5.12., 12.12.

Part III: Dejan Gajic and Stefan Czimek: The Einstein Equations: Initial data and dynamics
Dates: 06., 13., 20., and 27. February 2023

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