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

Nonconvex Optimization and the Curse of Local Minima - Lessons Learned from Orbital Tomography

Explore nonconvex optimization algorithms, focusing on quality of fixed points in orbital tomography. Gain insights into evaluating algorithm effectiveness beyond convergence speed.

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

Proximal Gradient Methods for Nonsmooth Nonconvex Minimax - A Unified Convergence Analysis

Explore proximal gradient methods for nonsmooth nonconvex minimax problems, analyzing convergence and complexity through a unified framework for parallel and alternating schemes.

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

How to Optimize a Schrödinger Bridge

Explore optimization techniques for Schrödinger Bridge problems, focusing on a novel geometric framework and Sinkhorn algorithm variants for efficient solutions in AI and diffusion models.

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

Computer-Aided Lyapunov Analyses and Counter-Examples to the Convergence of First-Order Optimization Methods

Explore computer-aided Lyapunov analyses and counter-examples for first-order optimization methods, focusing on constructive approaches and structural properties.

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

CCCP is Frank-Wolfe in Disguise - Connecting Optimization Methods

Uncover the surprising connection between CCCP and Frank-Wolfe methods, gaining insights and transferring convergence theory for nonconvex optimization problems.

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

Error Bounds for Mean-Payoff Markov Decision Processes

Explore optimal transport techniques for error bounds in reinforcement learning, focusing on mean-payoff Markov decision processes and stochastic fixed point iterations.

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

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