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

The Nonlinear Stability of Kerr for Small Angular Momentum

Explore the stability of Kerr black holes in general relativity, focusing on recent advancements for small angular momentum cases.

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

The Modified Energy Method for a Nonlocal Quasilinear Wave Equation

Explore nonlinear waves and relativity through the modified energy method for a nonlocal quasilinear wave equation in this advanced mathematics lecture.

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

Weakly Turbulent Solution to the Schrödinger Equation on the 2D Torus with Potential

Explore a smooth solution to the linear Schrödinger equation on a 2D torus, examining logarithmic H^1 Sobolev norm growth and infinite-time blowup using adapted CKSTT techniques.

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

Dispersion Estimates for Dirac Equations with Aharonov-Bohm Magnetic Fields

Explore dispersive properties of 2D Dirac operators with Aharonov-Bohm potentials, examining flow components and deducing sharp Strichartz estimates for advanced mathematical analysis.

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

Haunted Einstein-Yang-Mills Wormholes in Nonlinear Waves and Relativity

Explore infinite sequences of static spherically symmetric wormhole solutions in SU(2) Einstein-Yang-Mills equations, featuring phantom field "hauntings" in traversable tunnels between universes.

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

High-Order Moreau Envelope in the Nonconvex Setting: Framework and Algorithms

Explore high-order proximal operators and Moreau envelopes in nonconvex optimization, examining properties, algorithms, and convergence analysis for advanced mathematical applications.

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

A Fresh Look at Algorithms for Solving Smooth Multiobjective Optimization Problems

Explore new algorithms for smooth multiobjective optimization using linear programming to find decreasing directions, applicable to various constraint types and yielding substationary points.

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

Coordinate Descent Methods Beyond Separability and Smoothness

Explore advanced coordinate descent methods for complex optimization problems, covering nonseparable and nonsmooth functions, random proximal gradients, and smooth approximations.

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

Sum-of-Minimum Model: Joint Optimization of Specialized Models for Heterogeneous Data

Explore joint optimization of specialized models for heterogeneous data using the sum-of-minimum approach. Learn algorithm design, performance bounds, and applications in various machine learning tasks.

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

Kurdyka-Łojasiewicz Exponent for Hadamard-Difference-Parameterized Models

Explore Kurdyka-Łojasiewicz exponents in L1-regularized optimization, focusing on Hadamard difference parametrization and its impact on local convergence rates of gradient methods.

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

Toward a Grand Unified Theory of Accelerations in Optimization and Machine Learning

Explore acceleration mechanisms in optimization and machine learning, aiming to unify diverse approaches for a comprehensive mathematical theory.

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

Semi-Newton Method in Difference Programming

Explore a novel Newton-type algorithm for nonsmooth optimization problems, focusing on difference programming and its applications in structured optimization and practical problem-solving.

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

Revisiting Inexact Fixed-Point Iterations for Min-Max Problems - Stochasticity and Cohypomonotonicity

Explore advanced optimization techniques for constrained min-max problems, focusing on inexact fixed-point iterations and stochastic algorithms for nonconvex-nonconcave scenarios.

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

Kato Meets Bakry-Émery: Curvature Conditions in Riemannian Geometry

Explore the relationship between Bakry-Émery curvature-dimension and Kato condition on Ricci curvature, uncovering insights on Kato limit spaces and Riemannian manifolds.

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

Strong Convergence of Inertial Algorithms via Tikhonov Regularization

Explore inertial algorithms with Tikhonov regularization for optimization problems, examining strong convergence to minimum norm solutions and fast convergence rates for objective function values.

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