Institut des Hautes Etudes Scientifiques (IHES) Courses

Le problème du bicentralisateur de Connes - Histoire, motivations et résultats récents

Explorez le problème du bicentralisateur de Connes, son histoire et ses implications dans la théorie des facteurs de type III1. Découvrez les avancées récentes dans ce domaine mathématique complexe.

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

Schatten Properties of Commutators on Quantum Tori

Explore Schatten properties of commutators on quantum tori, characterizing them through Besov spaces and extending to Calderon-Zygmund operators in noncommutative settings.

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

Quantum Automorphism Groups of Some Classes of Graphs

Explore quantum symmetries in graphs, revealing hidden quantum behaviors and comparing classical and quantum automorphism groups through examples and recent computations.

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

Schoenberg Correspondence and Semigroup of k-(super)positive Operators

Explore Schoenberg correspondence and semigroups of k-(super)positive operators, extending LKGS theorem to characterize generators of various positive maps in quantum information theory.

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

Free Wreath Products as Fundamental Graph C*-algebras

Explore free wreath products of compact quantum groups, their operator algebras, and properties through graph C*-algebra constructions.

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

From the Littlewood-Paley-Stein Inequality to the Burkholder-Gundy Inequality

Explore optimal constants in Littlewood-Paley-Stein inequality through special diffusion semi-group construction, relating G-function to martingale square function in various cases.

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

Tracial and G-invariant States on Quantum Groups

Explore tracial and G-invariant states on quantum groups, examining connections between traceability and G-invariance in discrete quantum group C*-algebras.

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

Propriétés de relèvement pour les *-algèbres : du local au global ?

Explorez les propriétés de relèvement des C*-algèbres, du local au global. Examinez la relation entre LLP et LP, les caractérisations du LP, et les implications pour les algèbres WEP.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Non-commutative Pointwise Ergodic Theorem for Actions of Amenable Groups

Explore generalizations of Birkhoff's theorem for amenable group actions and von Neumann algebras, focusing on non-commutative maximal functions and operator families.

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

The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 2

Explore the Loewner energy's role in random conformal geometry, connecting SLE, Weil-Petersson quasicircles, and various mathematical branches. Gain insights into curve roundness and its implications.

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

Geometry and Physics of Covalent Network Glasses

Explore the mathematical modeling of glass transition in covalent network glasses, focusing on molecular agglomeration and stochastic processes to predict glass transition temperatures.

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

The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 1

Explore the Loewner energy's role in random conformal geometry, connecting SLE, Weil-Petersson quasicircles, and various mathematical branches. Gain insights into curve roundness and its implications across multiple fields.

• YouTube
• 1 hour 52 minutes
• Self-Paced
• Free Video

New Applications of the Reflection Equation Algebras

Explore new applications of Reflection Equation Algebras, including q-analogs of Schur-Weyl duality, Capelli formula, and Frobenius formula in quantum mathematics.

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

Cluster Duality and Non-Holomorphic Spectral Curves

Explore cluster duality, geometric interpretations of tropical points, and their connections to local systems on curves through graphs, Lagrangian coverings, and affine group-valued local systems.

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

On the Positivity of Meijer G-Functions

Explore positivity of Meijer G-functions, logarithmic infinite divisibility, and quasi infinite divisibility. Extend findings to Fox H-Functions.

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