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

Archimedean Modular Symbols and Automorphic Periods

Explore Archimedean modular symbols as cohomological interpretations of period integrals, defining automorphic periods and obtaining rationality results for L-functions.

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

Generalized Fourier Transforms for Exceptional Groups and Minimal Representations

Explore generalized Fourier transforms for exceptional groups and their connection to minimal representations in advanced mathematical analysis.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Poles of Eisenstein Series on General Linear Groups Induced from Two Speh Representations

Explore advanced techniques for determining poles of Eisenstein series on general linear groups, focusing on Speh representations and wave front sets.

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

A New Method to Determine the Regions of Holomorphy for Eisenstein Series Using the Franke Filtration

Explore a novel approach to determining holomorphy regions for Eisenstein series through the Franke filtration, focusing on automorphic forms and their applications.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

DNA Origamis - Their Folding Process and Their Interactions with Lipid Membranes

Explore DNA origami folding mechanisms and lipid membrane interactions, examining self-assembly uniqueness and electric field effects on water channel formation.

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

Nanopore Translocation of Entangled DNA and RNA Filaments

Explore nanopore translocation of DNA and RNA, focusing on polymer structural changes, unzipping mechanisms, and xrRNA resistance to degradation through simulations.

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

Charged for Attraction - How Biomolecular Condensates Pull Chromosomes Together

Discover how charged protein patches on chromosomes drive cellular organization through RNA-mediated attraction during cell division, combining simulations and theory.

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

Toward Phase Diagrams in Multidomain Protein Solutions In Vitro

Explore phase transitions in multidomain protein solutions, examining liquid-liquid separation and aggregation in engineered silk-like proteins through microscopy and thermodynamic analysis.

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

Thermodynamic Properties of Polymer Catenanes and Chainmails

Explore thermodynamic phase transitions in charged polymer catenanes and chainmails through theoretical analysis and simulation results from recent research.

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

Polymer Topology and Charged Soft Matter - A Tale of Rings

Explore the fascinating interplay between polymer topology and electric charge in ring-shaped macromolecules, uncovering unique rheological properties and cluster glass formation.

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

Anisotropic Interactions and Intermolecular Pose Exploration Using Subdivided Spheres

Explore anisotropic interactions between aspherical macromolecules using subdivided spheres for 6D lookup tables, bridging theory and experiment in protein osmotic virial coefficients.

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

Partial Regularity in Nonlocal Problems

Explore the theory of partial regular regularity for elliptic systems, focusing on extending classical local theory to nonlinear integrodifferential systems and providing tools for epsilon-regularity theorems in non-local settings.

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

Regularity and Dynamics for Nonlinear Diffusion Equations on Bounded Domains

Explore quantitative properties of fast diffusion and porous medium equations on bounded domains, including solution behavior characterization in Sobolev subcritical regime and dichotomy results in critical cases.

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

Evolution Problems with Perturbed 1-Laplacian Type Operators on Random Walk Spaces

Explore evolution problems with perturbed 1-Laplacian type operators on random walk spaces, as presented by Jose Mazon at the ESI Workshop on Degenerate and Singular PDEs.

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

Local and Nonlocal Zaremba Problems with Degenerate Weights

Explore the Zaremba problem with degenerate weights, examining both local and nonlocal formulations, existence results, and applications to fractal-like boundary conditions in PDEs.

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