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

The Long-Run Distribution of Stochastic Gradient Descent: A Large Deviations Approach

Explore the long-run behavior of stochastic gradient descent in non-convex problems, analyzing state space visitation patterns and energy level distributions.

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

Heaviside Composite Optimization and Complementarity Constraints by Progressive Integer Programming

Explore advanced optimization techniques for Heaviside composite functions and complementarity constraints using the progressive integer programming method.

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

Constraint Qualification and the Existence of Multipliers for Nonconvex Infinite-Dimensional Optimization Problems

Explore constraint qualifications and Lagrange multipliers for infinite-constrained optimization problems in Banach spaces, focusing on non-surjective derivative cases.

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

Progressive Decoupling of Dynamics in Convex Optimal Control

Explore progressive decoupling in convex optimization for optimal control, connecting classical calculus of variations with modern convex analysis and duality concepts.

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

Stable Blowup for the Higher-Dimensional Skyrme Model

Explore stable blowup mechanisms in higher-dimensional Skyrme models, focusing on finite-time blowup at self-similar rates in 5+1 dimensions compared to 3+1 dimensions.

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

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

Explore the failure of curvature-dimension conditions in sub-Finsler manifolds, focusing on recent proofs and implications for sub-Riemannian geometry and the Heisenberg group.

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

Plans, Derivations, and Currents in Metric Measure Spaces

Explore novel proofs and techniques in metric p-Sobolev spaces, connecting plans, derivations, and currents in metric measure spaces. Gain insights into advanced mathematical concepts.

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

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

Explore sharp concavity of isoperimetric profiles in RCD spaces, extending Bavard-Pansu's work on Ricci curvature bounds to non-smooth, finite-dimensional settings.

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

Markov Chain Curvature and Mixing

Explore Markov chain curvature and its impact on mixing processes in this mathematical analysis of non-smooth spaces and finite dimensions.

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

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