Synthetic Geometry Courses and Certifications

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Sobolev Calculus in Synthetic Lorentzian Geometry

Explore Sobolev calculus in synthetic Lorentzian geometry, focusing on time functions, weak lower differentials, and d'Alembert comparison results in measured Lorentzian length spaces.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lorentzian Length Spaces: An Introduction to Synthetic Lorentzian Geometry

Explore synthetic Lorentzian geometry foundations, focusing on time separation functions, curvature bounds, and applications in General Relativity, including recent developments in singularity theorems.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Fields Institute

Lorentzian Length Spaces - A Synthetic Approach to Lorentzian Geometry

Explore synthetic approaches to Lorentzian geometry through length spaces, offering new perspectives on spacetime structures and their applications in physics and mathematics.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Fields Institute

Introduction to the Riemannian Curvature Dimension Condition - Lecture 2

Explore advanced concepts in Riemannian geometry with Prof. Gigli, focusing on the Curvature Dimension condition and its applications in non-smooth settings.

• YouTube
• 1 hour 38 minutes
• On-Demand
• Free Video

Fields Institute

Introduction to the Riemannian Curvature Dimension Condition - Lecture 1

Explore the Riemannian Curvature Dimension condition with Professor Nicola Gigli, delving into advanced mathematical concepts for graduate-level understanding of non-smooth geometry.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Lorentzian Analog for Hausdorff Dimension and Measure

Explore a novel approach to geometric dimension in Lorentzian spaces, comparing it to Hausdorff dimension and examining applications in spacetime analysis and synthetic curvature bounds.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Synthetic Time-like Ricci Curvature Lower Bounds: The Isoperimetric Inequality

Explore synthetic timelike Ricci curvature lower bounds and their implications for isoperimetric inequality in Lorentzian synthetic spaces.

• YouTube
• 38 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Timelike Ricci Bounds and Einstein's Theory of Gravity in Non-Smooth Settings

Explore Lorentzian synthetic spaces, optimal transport theory, and timelike Ricci curvature bounds to characterize Einstein's equations in non-smooth spaces, with applications to gravity.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Metric Geometry of Spaces of Persistence Diagrams

Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Sharp Isoperimetric-Type Inequality for Lorentzian Spaces Satisfying Time-Like Ricci Curvature Lower Bounds

Explore sharp isoperimetric-type inequalities in Lorentzian spaces with time-like Ricci curvature bounds, including applications to black holes and cosmological space-times.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Unified Synthetic Ricci Curvature Lower Bounds for Riemannian and Sub-Riemannian Geometries

Explore unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian geometries through gauge metric measure spaces. Discover recent advances in metric measure and sub-Riemannian spaces.

• YouTube
• 45 minutes
• On-Demand
• Free Video