Institut des Hautes Etudes Scientifiques (IHES) Courses

A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Lecture 2

Explore a stable algebraic version of Gromov's angle shrinking problem and its application to dihedral rigidity conjecture, focusing on Fredholm index computation.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Point-Counting and the Zilber-Pink Conjecture - Lecture 2

Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.

• YouTube
• 1 hour 49 minutes
• On-Demand
• Free Video

Introduction to Numerical Relativity - Part 1

Explore Einstein's Field Equations through computational methods, covering 3+1 formulation, initial data, evolution, gauge choice, and extracting gauge-invariant quantities for astrophysical simulations.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Introduction to Numerical Relativity - Part 2

Explore computational methods for solving Einstein's Field Equations, covering 3+1 formulation, initial data, evolution, gauge choice, and extracting gauge-invariant quantities in astrophysical simulations.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Video

Point-Counting and the Zilber-Pink Conjecture - Lecture 1

Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Video

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 6

Explore modern techniques for analyzing flows of irregular vector fields, with applications to fluid dynamics and turbulence theory. Gain insights into nonlinear PDEs and Euler/Navier-Stokes equations.

• YouTube
• 1 hour 45 minutes
• On-Demand
• Free Video

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 5

Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.

• YouTube
• 1 hour 55 minutes
• On-Demand
• Free Video

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 4

Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.

• YouTube
• 1 hour 54 minutes
• On-Demand
• Free Video

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 3

Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.

• YouTube
• 1 hour 47 minutes
• On-Demand
• Free Video

Asymptotic Structure of Gravity and BMS Group at Spatial Infinity - Lecture 2

Explore asymptotic gravity structure at spatial infinity, BMS charges algebra, and connections to null infinity in this advanced theoretical physics lecture.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Asymptotic Structure of Gravity and BMS Group at Spatial Infinity - Part 1

Explore asymptotic structure of gravity, BMS charges, and angular momentum in asymptotically flat spacetimes using Hamiltonian methods at spatial infinity.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

Analytic Stacks: New Foundations for Analytic Geometry - Lecture 24

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

• YouTube
• 1 hour 54 minutes
• On-Demand
• Free Video

Generic Regularity in Obstacle Problems

Explore the classical obstacle problem, its free boundary, and recent developments in regularity theory with insights from renowned mathematician Alessio Figalli.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 2

Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.

• YouTube
• 1 hour 48 minutes
• On-Demand
• Free Video

Analytic Stacks: New Foundations for Analytic Geometry

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

• YouTube
• 1 hour 57 minutes
• On-Demand
• Free Video