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

Failure of the Curvature-Dimension Condition in Sub-Finsler Manifolds

Explore the failure of curvature-dimension conditions in sub-Finsler manifolds, examining smooth norms, Heisenberg groups, and measure contraction properties in non-smooth spaces.

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

Plans, Derivations, and Currents in Metric Measure Spaces

Exploración de espacios de Sobolev métricos p, equivalencia de definiciones y conexiones entre planes, derivaciones y corrientes en espacios de medida métrica.

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

Sharp Concavity of the Isoperimetric Profile Under Lower Ricci Bounds - Workshop on Synthetic Curvature Bounds

Explora la concavidad del perfil isoperimétrico en espacios RCD(K,N), generalizando resultados de Bavard-Pansu a geometrías no suaves y discutiendo cuestiones abiertas en dimensiones infinitas.

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

Markov Chain Curvature and Mixing

Explore Markov chain curvature and its impact on mixing processes in this mathematical analysis, delving into advanced concepts beyond finite dimensions.

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

Stochastic Algorithms for Constrained Continuous Optimization

Explore stochastic-gradient-based algorithms for constrained continuous optimization, including interior-point and sequential-quadratic-programming methods, with applications in machine learning and physics-informed problems.

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

Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization

Explores sample size estimates for risk-neutral optimization with semilinear elliptic PDEs, using SAA approach. Derives bounds on samples needed for accurate critical points, with numerical illustrations.

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

Nonmonotone Forward-Backward Splitting Method for Infinite-Dimensional Optimization Problems

Convergence analysis of nonmonotone forward-backward splitting for nonsmooth composite problems in Hilbert spaces, focusing on optimization in nonlinear PDEs with sparsity-promoting functionals.

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

A New Derivative-Free Method Using an Improved Under-Determined Quadratic Interpolation Model

Improved under-determined quadratic interpolation model for derivative-free optimization, considering trust-region iteration properties and model optimality. Enhances existing methods with implementation-friendly formula.

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

Scattering for Wave Equations with Sources and Slowly Decaying Data

Explora soluciones para ecuaciones de onda con fuentes de decaimiento polinomial, analizando campos de radiación prescritos y asintóticas homogéneas en el interior del cono de luz.

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

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

Explora el comportamiento asintótico tardío de soluciones de ecuaciones de onda en dimensiones espaciales impares, revelando diferencias clave entre escenarios lineales y no lineales en espaciotiempos dinámicos.

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

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

Exploración de la ecuación de Klein-Gordon no lineal en tres dimensiones, analizando el comportamiento global alrededor de multi-solitones y los desafíos en el seguimiento de modos inestables.

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

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

Explore stability and perturbation of self-similar solutions in modified Korteweg-de Vries equation, examining blowup dynamics and connections to fluid dynamics phenomena.

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

The Korteweg-de Vries Hierarchy in Rough Function Spaces

Explores wellposedness of KdV hierarchy in H^{-1}, extending Killip and Visan's work. Uses Miura map for Gardner hierarchy in L^2, proving weak solutions for all equations with L^2 initial data.

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

Dimension-Independent Functional Inequalities on Sub-Riemannian Manifolds

Explore gradient estimates and functional inequalities on sub-Riemannian manifolds using innovative techniques like tensorisation and quotients, bypassing traditional curvature bounds.

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

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

Exploración de límites inferiores sintéticos unificados de curvatura de Ricci para geometrías riemannianas y sub-riemannianas, basada en el estudio de espacios de medida métrica gauge.

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