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

Logical Analysis of Proofs in Non-Smooth Optimization Using Set-Valued Monotone Operators

Explore logical analysis techniques for proofs in non-smooth optimization through set-valued monotone operator theory and reverse mathematics applications.

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

From Brain Development and Reorganization to Reconstructing 77 Million Years of Brain Evolution

Explore groundbreaking geometric approaches to understanding brain architecture, disease-related reorganization, and evolutionary development across 77 million years through manifold learning and species analysis.

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

Lattice Theory of Noncrossing Partitions and Noncrossing Arc Diagrams - Lecture 3

Delve into advanced lattice theory concepts, exploring connections between Coxeter-Catalan combinatorics, representation theory, and dynamics through noncrossing partitions and arc diagrams.

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

Statistics on Monotonically Ordered Non-crossing Partitions

Delve into advanced mathematical concepts of non-crossing partitions, exploring sampling methods, nesting structures, and asymptotic behavior of combinatorial statistics in probability theory.

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

Annular Noncrossing Permutations in Non-commutative Probability

Explore advanced mathematical concepts of annular non-crossing permutations and their relationships to non-commutative probability, infinitesimal freeness, and random matrices.

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

Shifted Substitution in Non-Commutative Multivariate Power Series with Applications to Free Probability Theory

Delve into advanced mathematical concepts of non-commutative power series, exploring group laws, pre-Lie structures, and their applications in Voiculescu's free probability theory.

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

Non-crossing Partitions and Combinatorics: From Random Matrices to Free Probability Theory - Part 3

Delve into advanced combinatorics of maximal chains in non-crossing partition lattices, exploring connections between parking functions and Tamari lattice mathematics.

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

Rational Noncrossing Partitions and Associahedra

Explore rational generalizations of Catalan objects, focusing on noncrossing partitions and associahedra for coprime integers. Discover connections to rational Dyck paths and parking functions in this mathematical exploration.

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

Solvability of Lp Regularity Problem for Parabolic Operators with Rough Coefficients

Explore the solvability of Lp Regularity problem for parabolic operators with rough coefficients in this mathematical analysis presentation from the Workshop on Degenerate and Singular PDEs.

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

Some Recent Results on the Mixed Local and Nonlocal Problems

Explore recent advances in regularity results for mixed local and nonlocal problems, including higher Sobolev, Hölder regularity, and weak Harnack type estimates of solutions.

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

Gradient Regularity for a Class of Widely Degenerate Parabolic Equations

Explore gradient regularity in widely degenerate parabolic equations, focusing on mathematical analysis and solutions presented by Michael Strunk at the ESI Workshop on Degenerate and Singular PDEs.

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

Gradient Continuity for the Parabolic (1, p)-Laplace System with an External Force Term

Dive into the gradient continuity analysis of parabolic (1,p)-Laplace systems, exploring challenges with uniform parabolicity on facets and solutions for spatial gradient continuity despite anisotropic structures.

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

Characterisation of Weak Solutions to Gradient Flows of General Linear Growth

Delve into the characterisation of weak solutions to gradient flows with linear growth in this mathematical workshop presentation from ESI.

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

On a Sharp Interface Limit of the Kobayashi-Warren-Carter Energy

Explore the sharp interface limit of the Kobayashi-Warren-Carter energy system, its gradient flow, and the properties of minimizers in one-dimensional settings through mathematical analysis.

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

Interior Regularity Estimates for Fully Nonlinear Equations with Arbitrary Nonhomogeneous Degeneracy Laws

Delve into interior regularity estimates for fully nonlinear elliptic equations with arbitrary nonhomogeneous degeneracy laws, exploring conditions for continuously differentiable viscosity solutions.

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