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

Adjoint L-Values and the Tate Conjecture

Explore a strategy to prove the Tate conjecture on algebraic cycles for quaternionic Shimura varieties using twisted adjoint L-value formulas and theta base-change lifts.

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

Cohomology of Arithmetic Groups and Integral Structures on Automorphic Representations

Explore cohomology of arithmetic groups and integral structures on automorphic forms, covering locally algebraic representations and their role in Langlands' philosophy.

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

Some Conjectures on Arthur Packets and L-packets

Explore advanced conjectures extending tempered L-packet theory to non-tempered Arthur packets in the Langlands program, examining wave fronts and character singularities.

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

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