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#Synthetic Geometry

Showing: 9 courses
Fields Institute

Introduction to the Riemannian Curvature Dimension Condition - Lecture 2

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Explore advanced concepts in Riemannian geometry with Prof. Gigli, focusing on the Curvature Dimension condition and its applications in non-smooth settings.
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1 Lesons
1 hour 38 minutes
On-Demand
Free-Video
Fields Institute

Introduction to the Riemannian Curvature Dimension Condition - Lecture 1

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Explore the Riemannian Curvature Dimension condition with Professor Nicola Gigli, delving into advanced mathematical concepts for graduate-level understanding of non-smooth geometry.
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1 Lesons
1 hour 32 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Lorentzian Analog for Hausdorff Dimension and Measure

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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.
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1 Lesons
36 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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

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Explore synthetic timelike Ricci curvature lower bounds and their implications for isoperimetric inequality in Lorentzian synthetic spaces.
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1 Lesons
38 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

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Explore sharp isoperimetric-type inequalities in Lorentzian spaces with time-like Ricci curvature bounds, including applications to black holes and cosmological space-times.
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1 Lesons
49 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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

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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.
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1 Lesons
45 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

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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.
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1 Lesons
46 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lorentzian Length Spaces: An Introduction to Synthetic Lorentzian Geometry

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Explore synthetic Lorentzian geometry foundations, focusing on time separation functions, curvature bounds, and applications in General Relativity, including recent developments in singularity theorems.
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1 Lesons
51 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Metric Geometry of Spaces of Persistence Diagrams

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Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.
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1 Lesons
46 minutes
On-Demand
Free-Video