Institut des Hautes Etudes Scientifiques (IHES) Courses

Persistence Probabilities for Auto-Regressive Markov chains

Explore persistence probabilities and first crossing times for auto-regressive Markov chains, examining log-concavity conditions and Baxter-Spitzer factorization properties.

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

The Wronskians over Multidimension and Homotopy Lie Algebras

Explore multidimensional Wronskian determinants and their connection to homotopy Lie algebras, extending classical linear independence tests to higher dimensions and uncovering new algebraic structures.

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

On Universal Quadratic Inequalities for Minors of TNN Matrices

Discover universal quadratic inequalities for minors of totally non-negative matrices through advanced mathematical analysis and theoretical frameworks.

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

An Effective Proof of the p-curvature Conjecture for First-order Differential Equations

Discover an effective proof method for the p-curvature conjecture in first-order differential equations, connecting Honda's 1974 work with Kronecker's theorem through explicit bounds.

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

On the Integrality of Some P-Recursive Sequences

Discover a unified approach for analyzing integrality of P-recursive sequences through algebraic solutions of second-order recurrence relations with applications in combinatorics.

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

About Transfer Matrices

Discover advanced mathematical concepts as Maxim Kontsevich explores transfer matrices and their applications in modern mathematics and theoretical physics.

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

Arithmetic and Diophantine Geometry via Ergodic Theory and O-Minimality

Explore cutting-edge research in arithmetic geometry, Diophantine theory, ergodic systems, and Hodge theory through expert presentations honoring Emmanuel Ullmo's contributions.

• YouTube
• 21 hours 2 minutes
• Self-Paced
• Free Video

Discrete Subgroups of Lie Groups - Dynamics, Actions, Rigidity

Explore advanced mathematical concepts in discrete subgroups of Lie groups through expert-led mini-courses covering dynamics, rigidity theory, and geometric applications.

• YouTube
• 1 day 15 hours
• Self-Paced
• Free Video

Mathematics on the Crossroad of Centuries

Explore cutting-edge mathematics bridging algebra, geometry, topology, and physics through expert lectures honoring Maxim Kontsevich's groundbreaking contributions.

• YouTube
• 20 hours 55 minutes
• Self-Paced
• Free Video

Symmetries and Anomalies - A Modern Take

Explore quantum symmetries and anomalies across condensed matter, particle physics, and string theory through mathematical foundations and cutting-edge applications.

• YouTube
• 1 day 16 hours 14 minutes
• Self-Paced
• Free Video

Mathematics for and by Large Language Models

Explore the mathematical foundations of large language models and their applications in mathematical research through expert talks on synthetic data, training distributions, and ML-assisted mathematics.

• YouTube
• 5 hours 52 minutes
• Self-Paced
• Free Video

Flows of Irregular Vector Fields in Fluid Dynamics

Explore advanced mathematical techniques for analyzing irregular vector fields and their applications to fluid dynamics, turbulence theory, and nonlinear PDEs through modern flow theory.

• YouTube
• 10 hours 55 minutes
• Self-Paced
• Free Video

Analytic Stacks - New Foundations for Analytic Geometry

Explore revolutionary foundations for analytic geometry through light condensed abelian groups, analytic rings, and stacks with leading mathematicians Clausen and Scholze.

• YouTube
• 1 day 20 hours 4 minutes
• Self-Paced
• Free Video

Combinatorics and Arithmetic for Physics - Special Days Tenth Anniversary Edition

Explore discrete mathematics and number theory applications in theoretical physics through combinatorial structures, Hopf algebras, and computational methods.

• YouTube
• 19 hours 22 minutes
• Self-Paced
• Free Video

Arithmetic Algebraic Geometry in Memory of Jan Nekovář

Explore cutting-edge advances in arithmetic algebraic geometry through expert lectures honoring mathematician Jan Nekovář's contributions to the field.

• YouTube
• 22 hours 11 minutes
• Self-Paced
• Free Video