Institut des Hautes Etudes Scientifiques (IHES) Courses

Analytic Stacks - Lecture 3

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video

Analytic Stacks - Lecture 2

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.

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

Analytic Stacks - Lecture 1/24

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.

• YouTube
• 1 hour 50 minutes
• Self-Paced
• Free Video

Mock Plectic Points in Hilbert Modular Surfaces and Elliptic Curves

Explore the analogy between Hilbert modular surfaces and mock counterparts, examining plectic philosophy in mock Hilbert settings and its implications for elliptic curves of rank two over Q.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Period Relations for Arithmetic Automorphic Periods on Unitary Groups

Explore period relations for arithmetic automorphic periods on unitary groups, focusing on Petersson inner products and connections to L-function special values.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Shimurian Generalizations of Truncated Barsotti-Tate Groups - After V. Drinfeld

Explore Drinfeld's Shimurian analogs of truncated Barsotti-Tate groups, prismatic F-gauges, and their algebraicity in this advanced mathematical lecture.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

On the Cohomology of Shimura Varieties with Torsion Coefficients

Explore recent advances in Shimura varieties' cohomology with torsion coefficients, including Hodge-Tate period morphism geometry and local-global compatibility insights.

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

Hidden Symmetries of the Work of Jan Nekovář

Explorez les principes unificateurs de la recherche de Jan Nekovar, des systèmes d'Euler aux variétés de Shimura quaternioniques, en passant par les résultats de parité pour les fonctions L.

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

Conjectures on L-functions for Varieties over Function Fields and Their Relations

Explore conjectures on L-functions for varieties over function fields, focusing on abelian varieties and the BSD-rank conjecture. Examine relationships using rigid cohomology.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

De Rham Cohomology in Characteristic p - Advanced Topics

Explore advanced topics in de Rham cohomology of algebraic varieties in characteristic p, including stacky approaches and Steenrod operations' implications on spectral sequences.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Sato-Tate Conjecture for Bianchi Modular Forms

Explore potential automorphy results for Ramanujan and Sato-Tate conjectures in GL(2) over imaginary quadratic fields, extending previous work and introducing new mathematical concepts.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Eigenvarieties and Completed Cohomology in p-adic Automorphic Forms

Explore connections between eigenvarieties and p-adic cohomology representation theory, focusing on p-adic families of finite slope automorphic eigenforms.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Kummer Extensions: Applications to Generalized Cross-Ratios and Functions on Hilbert Schemes

Explore Kummer extensions in geometry and arithmetic, including generalized cross-ratios and functions on Hilbert schemes. Gain insights into advanced algebraic geometry concepts.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

On Geometric Construction of Artin Representation

Explore Serre's conjecture on integer-valued functions and Q_l-rational representations of finite groups acting on regular local rings.

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

Plectic Cohomology of Mixed Shimura Varieties and Stacks

Explore joint work on plectic cohomology of mixed Shimura varieties and stacks with Tony Scholl from the University of Cambridge.

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