Institut des Hautes Etudes Scientifiques (IHES) Courses

Weil Anima - 3/4

Explore homotopy-theoretic refinements of the Weil group in number theory, addressing deficiencies through cohomological considerations and connections to the Langlands program.

• YouTube
• 2 hours 3 minutes
• On-Demand
• Free Video

Réduire l'Impact des Séismes - Défis Scientifiques et Nouvelles Approches

Découvrez comment anticiper et réduire l'impact des séismes grâce aux nouvelles technologies : scénarios co-construits, détection par smartphones et intelligence artificielle.

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

Singular Supports in Equal and Mixed Characteristics - 4/4

Explore advanced algebraic geometry through singular supports of constructible sheaves, covering Beilinson's theory and extensions to mixed characteristics using Frobenius-Witt bundles.

• YouTube
• 2 hours 7 minutes
• On-Demand
• Free Video

A Proof of Onsager's Conjecture for the Incompressible Euler Equations

Discover how weak solutions to incompressible Euler equations can violate energy conservation, proving Onsager's 1949 conjecture about turbulent flows below 1/3-Hölder regularity.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

On the Wave Turbulence Theory of 2D Gravity Water Waves

Explore rigorous wave turbulence theory for 2D gravity water waves using deterministic energy estimates and probabilistic arguments for randomness propagation.

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

Anomalous Diffusivity and Regularity for Random Incompressible Flows

Explore anomalous diffusion in random incompressible flows using rigorous mathematical analysis and renormalization group techniques to understand long-time Brownian motion behavior.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

The Einstein Equation in Kähler Geometry

Explore how the Einstein equation simplifies in Kähler geometry and discover recent advances beyond Yau's theorem, including diameter estimates and convergence theorems.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Furstenberg Sets Estimates with Application to Restriction Theory

Explore advanced mathematical concepts connecting Kakeya sets, Hausdorff dimensions, and Fourier restriction theory through wave packet decompositions in this research seminar.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Two Methods for Deriving Singular Mean-Field Limits

Explore two mathematical methods for deriving mean-field limits in systems with singular interactions like Coulomb forces, including modulated energy and multiscale mollification approaches.

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

The Role of Spacetime Geometry in Gas Dynamics

Explore how spacetime geometry provides insights into wave equations and compressible Euler equations, covering shock formation, rarefaction waves, and singularity structures.

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

Open Issues in Gravitation

Explore cutting-edge challenges in General Relativity, from Yang-Mills connections to black hole physics and cosmological singularities with leading physicist Thibault Damour.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

A Physical-Space Approach to Global Asymptotics for Variable-Coefficient Klein-Gordon Equations

Discover a novel physical-space methodology for analyzing time decay and global asymptotics of variable-coefficient Klein-Gordon equations using "good commutators" and wave packet testing.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

The Soliton Resolution Conjecture for the Benjamin-Ono Equation

Discover the proof of the soliton resolution conjecture for the Benjamin-Ono equation, exploring how solutions decouple into solitons plus radiative terms in long-time asymptotics.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Late-Time Tails of Linear and Nonlinear Waves

Discover advanced methods for analyzing late-time asymptotic behavior of wave equations in odd dimensions, connecting nonlinear dynamics to black hole singularities in general relativity.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

The Nonlinear Stability of Kerr and Kerr-Newman Black Holes

Explore the nonlinear stability of Kerr and Kerr-Newman black holes through recent mathematical breakthroughs in Einstein equations and electromagnetic field dynamics.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video