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

Upper Bound for Wu's Correction to the Ground State Energy of a Dilute Bose Gas

Explore Wu's third-order correction to ground state energy in dilute Bose gases through rigorous mathematical analysis and thermodynamic limit considerations.

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

Seventy Years of the Mathematical Physics of the Bose Gas

Explore seven decades of mathematical physics research on Bose gas, from Dyson's pioneering 1957 work to modern proofs of Lee-Huang-Yang formulas and dilute limit asymptotics.

• YouTube
• 56 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

Feynman Integrals II - Parametric Representations (Schwinger, Feynman and Baikov)

Explore advanced parametric representations of Feynman integrals through Schwinger, Feynman, and Baikov methods in this specialized mathematical physics lecture.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Amplituhedra III - Combinatorics and Geometry for m=1,2

Explore advanced combinatorial and geometric structures of amplituhedra for specific cases m=1,2 in this specialized mathematics lecture from ESI's algebraic geometry programme.

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

Kinematic Varieties II - Gram Matrices

Explore advanced algebraic geometry through kinematic varieties and Gram matrices in this specialized mathematical physics lecture.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Amplituhedra II - Amplituhedron Basics and Big Questions

Explore advanced mathematical concepts in amplituhedra theory, covering fundamental principles and major open questions in this cutting-edge field of algebraic geometry.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Amplituhedra I

Explore the mathematical foundations of amplituhedra in this advanced physics lecture from ESI's amplitudes and algebraic geometry program.

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

Feynman Integrals I - Feynman Integrals and Integration by Parts Identities

Discover Feynman integrals and integration by parts identities through advanced mathematical physics techniques for amplitude calculations in algebraic geometry.

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

Singular Limits for PDE in Biology

Explore singular limits in biological PDEs, covering diffusive enzyme reactions and plant-growth dynamics with autotoxicity through advanced mathematical techniques and convergence analysis.

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

How Spatial Patterns Can Lead to Less Resilient Ecosystems

Discover how spatial vegetation patterns may actually reduce ecosystem resilience through convective instabilities, challenging traditional ecological theories with new mathematical models.

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