Erwin Schrödinger International Institute for Mathematics and Physics (ESI) Courses

Looking for p-Energy Forms in Cheeger Spaces

Explore p-energy forms in Cheeger spaces without relying on gradients. Learn about constructing these forms using characteristic features of Cheeger metric measure spaces.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Riesz Transforms for Dirichlet Spaces Tamed by Distributional Curvature Lower Bounds

Explore Riesz transforms in tamed Dirichlet spaces, examining Lp-boundedness under distributional curvature lower bounds and gaugeability conditions.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Sobolev Spaces in Extended Metric-Topological Measure Spaces

Explore Sobolev spaces in extended metric-topological measure spaces, focusing on Cheeger energy construction and properties in this general framework.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Non-Regular Spacetime Geometry via Metric Measure Geometry

Explore non-regular spacetime geometry using metric geometry, extending Lorentzian geometry beyond classical differential geometry for low-regularity spacetimes and general spaces.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Integral Varadhan Formula for Nonlinear Heat Flow on Measured Finsler Manifolds

Explore integral Varadhan formula for nonlinear heat flow on measured Finsler manifolds, examining particle probability and distance relationships in geometric analysis.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Dimension-Independent Functional Inequalities on Sub-Riemannian Manifolds

Explore gradient estimates and functional inequalities on sub-Riemannian manifolds, focusing on techniques like tensorisation and quotients for spaces without curvature bounds.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Rigidity of Mass-Preserving 1-Lipschitz Maps from Integral Current Spaces into Euclidean Spaces

Explore rigidity of mass-preserving 1-Lipschitz maps from integral current spaces to Euclidean balls, proving isometry conditions and discussing stability of positive mass theorem for graphical manifolds.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

Formation of Quiescent Big Bang Singularities

Explore general relativity's big bang singularities, recent stability results, and a new condition for big bang formation in Einstein-non-linear scalar field settings.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Extremal Critical Collapse in Gravitational Systems

Explore the formation of extremal black holes in gravitational collapse, challenging the third law of black hole thermodynamics and introducing the concept of extremal critical collapse.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Scattering for Wave Equations with Sources and Slowly Decaying Data

Explore scattering solutions for wave equations with polynomially decaying sources, analyzing radiation fields and asymptotic behavior near the lightcone in nonlinear wave contexts.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Late Time Tail of Waves on Dynamic Asymptotically Flat Spacetimes of Odd Space Dimensions

Explore late time asymptotic behavior of wave equations in odd spatial dimensions, uncovering new insights for dynamic backgrounds and nonlinear cases. Gain understanding of black hole interiors.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Initial Classification of Global Behavior Around Multi-Solitons for the Nonlinear Klein-Gordon Equation

Explore nonlinear Klein-Gordon equation's global behavior near multi-solitons, focusing on unstable mode tracing and energy transfer mechanisms in three-dimensional space.

• YouTube
• 49 minutes
• Self-Paced
• Free Video