Mathematics Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Algebraic Structures in Perturbative Quantum Field Theory

Explore algebraic structures in perturbative quantum field theory through expert lectures on Feynman integrals, Hopf algebras, renormalization, and mathematical physics connections.

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

Institut des Hautes Etudes Scientifiques (IHES)

Motivic, Equivariant and Non-commutative Homotopy Theory - Summer School 2020

Explore advanced topics in motivic, equivariant homotopy theory and non-commutative geometry through expert lectures covering latest developments in mathematical foundations and applications.

• YouTube
• 1 day 9 hours 42 minutes
• Self-Paced
• Free Video

Institut Henri Poincaré

Reinventing Rational Points

Explore advanced techniques in arithmetic geometry, from Brauer-Manin obstructions to counting rational points on algebraic varieties through analytic and geometric methods.

• YouTube
• 2 days 3 minutes
• Self-Paced
• Free Video

Institut Henri Poincaré

Model Theory, Combinatorics and Valued Fields

Explore advanced model theory applications in combinatorics and valued fields through rigorous mathematical analysis and cutting-edge research developments.

• YouTube
• 2 days 2 hours 27 minutes
• Self-Paced
• Free Video

Institut Henri Poincaré

Combinatorics and Interactions - Asymptotic Representation Theory, Random Maps, and Enumerative Geometry

Explore advanced combinatorics through asymptotic representation theory, random maps, dimer models, and enumerative geometry in this comprehensive research trimester program.

• YouTube
• 3 days 8 hours 29 minutes
• Self-Paced
• Free Video

Institut Henri Poincaré

Random Walks and Asymptotic Geometry of Groups

Explore advanced mathematical concepts connecting random walks with asymptotic geometry of groups through expert lectures from leading researchers in the field.

• YouTube
• 16 hours 47 minutes
• Self-Paced
• Free Video

ICTP Condensed Matter and Statistical Physics

Physics of Complex Systems - Spring College

Explore complex systems through statistical physics, random matrices, biological optimization, thermodynamics, and bacterial physiology in this intensive program from leading researchers.

• YouTube
• 2 days 9 hours 43 minutes
• Self-Paced
• Free Video

NCCR SwissMAP

Integrability in Condensed Matter Physics and Quantum Field Theory

Explore advanced mathematical techniques in integrable systems, from spin chains to quantum field theory, through expert lectures on Bethe ansatz, conformal bootstrap, and modern applications.

• YouTube
• 1 day 7 hours 12 minutes
• Self-Paced
• Free Video

NCCR SwissMAP

Master Class in Geometry, Topology and Physics

Explore advanced mathematical physics through algebraic geometry, symplectic geometry, quantum topology, field theory, and Poisson geometry in this intensive master class series.

• YouTube
• 1 week 20 hours 28 minutes
• Self-Paced
• Free Video

IPhT-TV

Group Theory in a Nutshell for Physicists

Master group theory fundamentals through Anthony Zee's comprehensive physics-focused approach across five detailed sessions.

• YouTube
• 9 hours 6 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Geometry for Higher Spin Gravity - Conformal Structures, PDEs, and Q-manifolds

Explore advanced mathematical frameworks connecting higher-spin gravity, conformal geometry, and quantum field theory through expert lectures on Cartan geometries, holography, and PDEs.

• YouTube
• 2 days 15 hours 48 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups (2025)

Explore cutting-edge developments in hyperbolic geometry and group theory through expert lectures and hands-on minicourses from leading mathematicians worldwide.

• YouTube
• 1 day 6 hours 39 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Numerical Methods for Partial Differential Equations (2022)

Master advanced computational techniques for solving partial differential equations through rigorous mathematical analysis and practical implementation methods.

• YouTube
• 1 day 4 hours 26 minutes
• Self-Paced
• Free Video

Centre International de Rencontres Mathématiques

Computational Time-Frequency and Coorbit Theory

Explore advanced mathematical analysis through computational time-frequency methods, coorbit theory, and function spaces with applications to wavelets, Gabor frames, and operator theory.

• YouTube
• 12 hours 20 minutes
• Self-Paced
• Free Video

Centre International de Rencontres Mathématiques

Number Theory and its Applications to Cryptography

Explore advanced number theory applications to cryptography through elliptic curves, Frobenius distributions, and pseudorandom generators in this comprehensive mathematical semester.

• YouTube
• 20 hours 5 minutes
• Self-Paced
• Free Video