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Talk

Saturday, October 1, 2022 10:00

IMPRS-Ringvorlesung: Winter semester 2022/2023

Tobias Ried
Florentin Münch
Dejan Gajic
Stefan Czimek

E1 05 (Leibniz-Saal)

Abstract

About this lecture
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.

Topics

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

Date and time info
Mondays 10.30-12.00 (please note special dates and rooms at the lectures)

Audience
IMPRS students and others

Language
english

Links

lecture

10/1/22 1/31/23

Regular lectures Winter semester 2022-2023

MPI for Mathematics in the Sciences / University of Leipzig see the lecture detail pages

See Details

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail