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Lorentzian Length Spaces: An Introduction to Synthetic Lorentzian Geometry

Offered By: Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube

Tags

General Relativity Courses Optimal Transport Courses Ricci Curvature Courses Lorentzian Geometry Courses Synthetic Geometry Courses

Course Description

Overview

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Explore the foundations of synthetic Lorentzian geometry in this 51-minute talk by Michael Kunzinger, presented at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) as part of the Thematic Programme on "Geometry beyond Riemann: Curvature and Rigidity." Delve into the theory of Lorentzian (pre-)length spaces, focusing on the time separation function as the fundamental object. Discover how basic notions are derived from this function, including the definition of sectional curvature bounds through triangle comparison. Learn about the adaptation of methods from metric measure geometry and optimal transport to implement synthetic timelike Ricci curvature bounds. Gain insights into the application of these concepts in General Relativity, including recent developments in synthetic versions of Hawking's singularity theorem and vacuum Einstein equations.

Syllabus

Michael Kunzinger - Lorentzian length spaces


Taught by

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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