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

Global Weak Solutions to a Navier-Stokes/Mullins-Sekerka System with Different Densities

Explore global weak solutions for two-fluid flow with unmatched densities using coupled Navier-Stokes/Mullins-Sekerka systems and novel mathematical frameworks.

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

Linear Stability of the Self-Similarly Shrinking Lens

Explore linear stability analysis of self-similar shrinkers in 2D multiphase mean curvature flow, focusing on the lens example and entropy-based stability methods.

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

Minimality of the Hopf Map for the Faddeev-Skyrme Energy

Explore the mathematical proof demonstrating why the Hopf map achieves minimal energy in the Faddeev-Skyrme model through advanced topological analysis.

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

The Epsilon-Regularity Theorem for Brakke Flows Near Triple Junctions

Explore epsilon-regularity for Brakke flows near triple junctions, extending Simon's 1993 minimal surface theory to parabolic mean curvature flows with applications to grain boundaries.

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

Equivalence of Weak Solution Concepts for Mean Curvature Flow

Explore the equivalence between viscosity and variational weak solution concepts for mean curvature flow, revealing how geometric and variational approaches converge in this fundamental evolution equation.

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

Crystalline Elastic Flow of Polygonal Curves

Explore crystalline elastic flow of polygonal curves, covering long-time existence, uniqueness, global evolution, convergence to stationary configurations, and classification of solutions.

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

On the Free Boundary Elastic Flow

Explore the length-preserving elastic flow with free boundaries on hypersurfaces, examining nonlocal evolution equations and global existence under non-flatness assumptions.

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

DLR Equations for the Superstable Bose Gas at any Temperature and Activity

Explore DLR equations for superstable Bose gas systems across all temperature and activity ranges in this advanced mathematical physics lecture from ESI's quantum many-body workshop.

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

The Charge Gap, the Neutral Gap, and Fractional Quantum Hall Systems

Explore fundamental inequalities connecting charge and neutral gaps in quantum many-body systems, with applications to fractional quantum Hall pseudo-potentials and spectral analysis.

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

Stability of Matter - The 50th Anniversary of the Lieb-Thirring Proof

Discover the foundational Lieb-Thirring proof on stability of matter through a non-technical introduction to their 1975 breakthrough and its lasting impact on mathematical physics.

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

Third Order Correction to the Ground State Energy of a Bose Gas in the Gross-Pitaevskii Regime

Explore advanced mathematical physics techniques for computing third-order energy corrections in Bose gases using renormalization and correlation methods.

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

Long-time Validity of Bogoliubov Theory

Explore the uniform-in-time validity of Bogoliubov approximation for weakly interacting Bose gases and quantum fluctuations around Bose-Einstein condensates.

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

Derivation of Phi 4 Over 3 Theory from Many-Body Quantum Mechanics

Explore the mathematical derivation of phi 4/3 theory from many-body quantum mechanics in this advanced physics lecture from ESI's quantum systems workshop.

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

Euclidean Field Theories as Limit of Interacting Bose Gases

Explore the rigorous mathematical derivation of Euclidean field theories from interacting Bose gases, focusing on quartic interactions in two dimensions and extending previous torus results.

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

BEC with Optimal Rate in the Gross-Pitaevskii Limit

Explore recent proofs of complete Bose-Einstein condensation with optimal error bounds for approximate ground states and their time-evolution in the Gross-Pitaevskii limit.

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