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

Synthetic Time-like Ricci Curvature Lower Bounds: The Isoperimetric Inequality

Explore synthetic timelike Ricci curvature lower bounds and their implications for isoperimetric inequality in Lorentzian synthetic spaces.

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

Timelike Ricci Bounds and Einstein's Theory of Gravity in Non-Smooth Settings

Explore Lorentzian synthetic spaces, optimal transport theory, and timelike Ricci curvature bounds to characterize Einstein's equations in non-smooth spaces, with applications to gravity.

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

A Nonsmooth Approach to Einstein's Theory of Gravity

Explore a nonsmooth approach to Einstein's gravity theory, focusing on reformulating curvature concepts and developing a synthetic null energy condition for Lorentzian spaces.

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

Our Changing Climate System

Explore the ongoing climate change, its impacts, and the urgent need for global action with insights from glaciologist Georg Kaser on irreversible changes and the Paris Agreement.

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

Phase Transitions and Self-Assembly in Active Matter

Explore phase transitions and self-assembly in active matter systems, from bird flocks to nanorobots. Analyze statistical models, emergent behaviors, and out-of-equilibrium dynamics in collective motion phenomena.

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

MaZe: A New Approach for Simulating Adiabatic Systems - Lecture

Explore MaZe, a novel approach for simulating adiabatic systems in physics. Learn about its applications in first principles simulations, polarizable systems, and ionic transport studies.

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

Minimization Problems for the Axisymmetric Neo-Hookean Energy

Explore minimization problems for axisymmetric neo-Hookean energy, focusing on existence of minimizers, energy concentration, and bounds for relaxed energy in critical Sobolev cases.

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

Characterisation of Area-Strict Limits of Planar BV Homeomorphisms

Explore area-strict limits of planar BV homeomorphisms, focusing on cavitations, fractures, and the no-crossing condition in elastic deformations.

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

Injectivity in Second-Gradient Nonlinear Elasticity

Explore injectivity in second-gradient nonlinear elasticity, delving into advanced mathematical concepts and their applications in materials science.

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

Existence of Solutions for the 2D Signorini-Coulomb Problem

Explore solutions for 2D Signorini-Coulomb problem in static contact with Coulomb friction, comparing isotropic and anisotropic elasticity using Leray-Lions operator approach.

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

Regularity, Cavitation and Harmonic Dipoles in Nonlinear Elasticity

Explore regularity, cavitation, and harmonic dipoles in nonlinear elasticity. Analyze Sobolev maps, gradient determinants, and integrability exponents to understand deformation behavior and singularities.

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

Sobolev Homeomorphic Extensions in Geometric Analysis and Nonlinear Elasticity

Explore Sobolev homeomorphic extensions in geometric analysis, focusing on boundary map properties and their implications for nonlinear elasticity and higher-dimensional problems.

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

Fully Discrete Approximation Schemes for Rate-Independent Crack Propagation

Explore convergence analysis of space-time discrete approximation schemes for rate-independent crack propagation in brittle elastic bodies, focusing on Griffith fracture criterion and local energy minimizers.

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

Non-interpenetration in Thin-film Models of Elastic Solids

Explore non-interpenetration in thin-film models for elastic solids, focusing on dimension reduction, membrane regimes, and suitable conditions for preventing material penetration.

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

De Rham Algebras of Closed Quasiregularly Elliptic Manifolds are Euclidean

Explore quasiregular mappings and de Rham cohomology in closed manifolds, leading to a homeomorphic classification of certain 4-manifolds.

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