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

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
• On-Demand
• Free Video

µ-ellipticity and Nonautonomous Integrals

Delve into µ-ellipticity in degenerate elliptic forms, exploring recent advances in Schauder theory for anisotropic, nonautonomous functionals with Hölder continuous coefficients and their applications to area-type integrals.

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

Noncrossing Partitions of a Marked Surface

Explore noncrossing partitions of marked surfaces, generalizing from disks and annuli to broader topological contexts, with insights into their lattice structures and connections to Coxeter groups and representation theory.

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

Non-crossing Partitions and Webs

Explore the connection between non-crossing partitions and webs, focusing on hourglass plabic graphs as a new approach to SL(4)-web bases and their relationship to Kreweras complements.

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

Shi-like and Catalan-like Deformations for Restricted Reflection Arrangements

Delve into the mathematical exploration of Shi and Catalan arrangements as deformations of braid arrangements, connecting to noncrossing partitions, parking functions, and Weyl group theory.

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

Investigation on Minimal Surfaces, Biharmonic Submanifolds, and their Applications in Discrete Geometry

Explore advanced mathematical concepts of minimal hypersurfaces, biharmonic submanifolds, and their applications in discrete geometry and shape analysis through groundbreaking research findings.

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

Parking Functions as Noncrossing Cosets - From Stanley to Cohen-Macaulay Properties

Explore the mathematical relationship between parking functions and noncrossing partitions, examining their topological properties and connections to symmetric group actions and Cohen-Macaulay posets.

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

Conjecture on Descents, Inversions and the Weak Order in Coxeter Systems

Explore advanced mathematical concepts of Coxeter systems, examining partitions, left descents, and weak order relationships through an innovative conjecture on descent distributions.

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

The Poincare-Extended AB-Index in Combinatorial Topology

Explore the intersection of Igusa zeta functions, combinatorics, and poset topology through a novel polynomial that unifies hyperplane arrangements and lattice structures.

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

Double Bialgebra of Noncrossing Partitions

Delve into advanced mathematical concepts exploring double bialgebra structures and their relationship with noncrossing partitions in this theoretical mathematics presentation.

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

Non-crossing Partitions and Combinatorics: From Random Matrices to Free Probability Theory - Part 2

Delve into advanced mathematical concepts of free cumulants, non-crossing partitions, and their connection to random matrix theory through Schur-Weyl duality and unitary group integration.

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

Lattice Theory of Noncrossing Partitions and Noncrossing Arc Diagrams - Lecture 2

Delve into advanced lattice theory concepts, exploring Coxeter-Catalan combinatorics, representation theory, and the connections between noncrossing partitions and c-Cambrian lattices.

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

Combinatorial Identities for Partition Sets and Limit Theorems in Free Probability

Explore combinatorial identities for partition sets and their connections to limit theorems, finite free convolutions, and asymptotic behavior of Unitary Hermite and Laguerre Polynomials.

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

The Chain Polynomials of Noncrossing Partition Lattices are Real-Rooted

Delve into advanced mathematical concepts exploring chain polynomials in noncrossing partition lattices, focusing on finite Coxeter groups and their h-polynomial formulas.

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

Some Reducibilities in Computability Theory

Explore recent results on reducibilities and degree structures in computability theory, covering interactions with classical computability, constructive mathematics, and reverse mathematics.

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