Institut des Hautes Etudes Scientifiques (IHES) Courses

Scalar Curvature via Dirac Eigenvalues

Explore advanced differential geometry connecting scalar curvature to Dirac eigenvalues, covering Llarull's theorem, Geroch conjecture, and Yamabe invariant relationships.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Bosonization of Fermi Surface - The Method of Coadjoint Orbits - 3/3

Explore advanced field-theoretical reformulation of Landau Fermi liquid theory using coadjoint orbits and nonlinear bosonization methods for condensed matter physics.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

Elliptic Surfaces, Equidistribution, and Bifurcations

Explore arithmetic intersection numbers of elliptic surface sections over number fields, Bogomolov-type extensions, and connections to Zilber Pink conjectures in this advanced mathematics lecture.

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

Mathematical Approaches to Conformal Bootstrap

Explore conformal field theory's operator algebra and its mathematical framework, focusing on lightcone bootstrap results and key open problems in theoretical physics.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video

Problèmes Ouverts et Progrès Récents en Géométrie Spectrale Hyperbolique

Découvrez les avancées récentes sur le trou spectral des surfaces hyperboliques et leurs liens avec la théorie des cordes et les quasi-cristaux en géométrie spectrale.

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

Mathematical Bootstrap - From Conformal Fields to L-Functions

Explore the mathematical bootstrap connecting conformal field theory to number theory, with applications to spectral gaps and L-functions.

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

p-adic Motives and Special Values of Zeta Functions

Explore unconditional formulation and proof of Artin-Tate conjectures for zeta functions using $F$-Gauges theory and stable Bockstein characteristics in algebraic geometry.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Geometric Aspects of the p-adic Locally Analytic Langlands Program

Explore geometric aspects of p-adic Langlands program, focusing on locally analytic representations as sheaves on variants of Fargues-Scholze's stack of G-bundles.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Non-Archimedean Motives IV

Explore advanced non-Archimedean motives over adic spaces, covering six-functor formalism, continuity properties, and applications to p-adic cohomology theories.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Uniqueness and Functoriality of Igusa Stacks

Explore the uniformization of p-adic Shimura varieties through Igusa stacks, examining their uniqueness via deformation theory and p-adic Hodge theory.

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

Towards mod p Local Global Compatibility for Partial Weight One Hilbert Modular Forms

Explore advanced number theory through mod p Hilbert modular forms, Galois representations, and local-global compatibility conjectures for totally real fields.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Non-Archimedean Motives III

Explore advanced non-Archimedean motives over adic spaces, focusing on six-functor formalism, continuity properties, and applications to p-adic cohomology theories.

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

Geometric Aspects of the p-adic Locally Analytic Langlands Correspondence III

Explore geometric aspects of p-adic Langlands correspondence, focusing on moduli stacks of Galois representations and their geometric properties in this advanced mathematical lecture.

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

Igusa Stacks - Lecture 4

Explore advanced techniques using Igusa stacks to study Shimura variety cohomology through categorical local Langlands program applications.

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

On the Mod p and p-adic Jacquet-Langlands Correspondence for Drinfeld Towers

Explore advanced applications of Mann's 6 functor formalism to mod p and p-adic cohomology of Drinfeld towers, featuring collaborative research insights.

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