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

Supersolids in Magnetic Gases - From Roton Softening to Quantum Vortices

Explore supersolid quantum states in magnetic gases, covering roton softening, phase transitions, symmetry breaking, and quantized vortices in rotating systems.

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

Dilute Bosons in Two Dimensions

Explore the mathematical physics of dilute Bosons in 2D, covering the Lee-Huang-Yang formula, excitation spectrum, and key differences from 3D systems.

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

Semiclassical Analysis of Mean-Field Type Equations

Explore semiclassical analysis techniques for mean-field equations in quantum many-body systems and Bose-Einstein condensation through advanced mathematical physics methods.

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

The Effective Mass of the Fröhlich Polaron at Strong Coupling

Explore the Fröhlich polaron model and discover how charged particles interact with polarizable environments, focusing on the rigorous proof of the Landau-Pekar formula for effective mass.

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

Exchange Interactions and Cuprate Superconductivity

Explore quantum exchange interactions in fermion-boson systems and their role in high-temperature cuprate superconductivity through mathematical physics analysis.

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

The Huang-Yang Conjecture for the Low Density Fermi Gas

Discover the rigorous proof of the 1957 Huang-Yang conjecture on ground state energy of dilute Fermi gases, revealing universal correlation energy dependence on scattering length.

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

Tunnelling Formulae for Magnetic Operators

Explore advanced mathematical analysis of quantum tunnelling effects in magnetic fields, covering semiclassical theory, complex phase challenges, and recent breakthroughs in magnetic operator research.

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

Introduction to Brakke's Mean Curvature Flow - Part 3

Dive into advanced geometric analysis with Brakke's mean curvature flow theory, exploring free boundary problems through rigorous mathematical frameworks and analytical techniques.

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

Kinematic Varieties I - Massless Particles

Explore kinematic varieties and their applications to massless particles in this advanced mathematics and physics lecture by renowned algebraist Bernd Sturmfels.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

On the Mirror Langevin Diffusions

Explore Mirror Langevin Diffusions, a new family of diffusions on Hessian manifolds connecting Wasserstein gradient flows, Schrödinger bridges, and modern sampling techniques.

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

Amplituhedra IV - Techniques for Higher m

Explore advanced mathematical techniques for analyzing amplituhedra with higher m values in this specialized algebraic geometry lecture from ESI's amplitudes programme.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Feynman Integrals IV - Integrand Analysis for Polylogs and Beyond

Delve into advanced integrand analysis techniques for polylogarithmic functions and their extensions in Feynman integral calculations within quantum field theory.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Kinematic Varieties IV - Lines in 3-Space

Explore advanced algebraic geometry through kinematic varieties, focusing on the mathematical structure of lines in three-dimensional space with expert insights.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Kinematic Varieties III - Let's Get Real

Explore advanced kinematic varieties with focus on real algebraic geometry applications in particle physics and scattering amplitudes theory.

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

Feynman Integrals III - Differential Equations and Canonical Bases

Master differential equations and canonical bases for Feynman integrals in this advanced mathematical physics lecture from ESI's amplitudes and algebraic geometry programme.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video