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

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

Gross-Pitaevskii Equation for Supersolids

Explore the mathematical physics of supersolids through the Gross-Pitaevskii equation, examining phase transitions and periodic solutions in infinite Bose gas condensates.

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

Damping of Phonons at Low Temperature

Explore phonon decay rates in interacting Bose gas at low temperatures, covering Beliaev and Landau damping mechanisms through Bogoliubov approximation and Fermi Golden Rule.

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

About the Observation of Bose-Einstein Condensation in Liquid 4He

Explore the century-long journey from Einstein's 1925 prediction to experimental observation of Bose-Einstein condensation in superfluid helium, including neutron scattering breakthroughs.

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

Recent Developments in the Analysis of Bose Gases at Positive Temperature

Explore advanced mathematical physics techniques for analyzing weakly interacting Bose gases, covering Gibbs states, particle distributions, and thermodynamic limits.

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

Exact Solution of Many-Body Problems Using Quantum Monte Carlo - Applications to Ultracold Atoms

Explore quantum Monte Carlo methods for solving many-body Bose particle systems, covering ultracold atoms, dipolar systems, and Lieb-Liniger model applications.

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

Who Acquires Infections from Whom - Neutral Allele Frequencies Can Tell

Discover how neutral allele frequencies reveal infection transmission patterns and pathways in biological systems through mathematical analysis.

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

Some Reducibilities in Computability Theory

Explore recent results on reducibilities and degree structures in computability theory, covering interactions with classical computability, constructive mathematics, and reverse mathematics.

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

Generic Muchnik Reducibility

Explore generic Muchnik reducibility extending classical reducibility to uncountable structures, mixing descriptive set theory with forcing constructions in computable model theory.

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

Higher Type Recursion in Transfinite Computational Models

Explore higher type recursion through infinite time Turing machines and discover analogies with Kleene's Type 2 computation model in this advanced mathematical talk.

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