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

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

Perturbation at Blow Up of Self-Similar Solution for Modified Korteweg-de Vries Equation

Explore stability and perturbation of self-similar solutions' blowup dynamics in the modified Korteweg-de Vries equation, with applications to fluid dynamics and vortex patch formation.

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

The Korteweg-de Vries Hierarchy in Rough Function Spaces

Explore the Korteweg-de Vries hierarchy in rough function spaces, focusing on wellposedness and the Miura map's role in translating to the Gardner hierarchy.

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

Modified Scattering for the Three Dimensional Maxwell-Dirac System

Explore global well-posedness and modified scattering for the massive Maxwell-Dirac equation in R3+1, focusing on small, localized initial data and novel approaches to Dirac equations.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Finite Point Blowup for the Critical Generalized Korteweg-de Vries Equation

Explore finite point blowup in critical generalized KdV equations, uncovering new blow-up dynamics and rates. Gain insights into recent advancements in nonlinear wave theory.

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

Oppenheimer-Snyder Type Collapse for the Einstein-Vlasov System

Explore gravitational collapse approximation using Einstein-Vlasov system, extending Oppenheimer-Snyder's work on dust balls to understand black holes and cosmic censorship.

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

New Developments on Asymptotically Leaky Boundaries

Explore new developments in asymptotically leaky boundaries, focusing on recent research and ongoing work in Carrollian physics and holography.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video