Institut des Hautes Etudes Scientifiques (IHES) Courses

Weil Anima - Part 4

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

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

How Hard is the Theorem of Stolz - Metrics and Scalar Curvature in Spin Manifolds

Delve into the complexity of Stolz's theorem on positive scalar curvature metrics, exploring metric deformations and manifold transformations through groundbreaking mathematical research findings.

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

Localization Theory for Harish-Chandra Bimodules in Positive Characteristic

Delve into advanced algebraic group theory, exploring Harish-Chandra bimodules, equivariant coherent sheaves, and their connections to representation theory in positive characteristic mathematics.

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

On the Left Adjoint of mod p Smooth Parabolic Induction

Delve into advanced mathematical concepts exploring parabolic induction functors, focusing on left adjoint properties and their behavior with algebraic weights in p-adic field extensions.

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

Relative Poincaré Duality in Non Archimedean Geometry

Delve into advanced mathematical concepts exploring relative mod-p Poincaré duality in rigid-analytic varieties, featuring novel trace map constructions and diagrammatic proofs for smooth morphisms.

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

q-Higgs Modules and the Nygaard Filtration in Prismatic Cohomology

Delve into advanced mathematical concepts of prismatic crystals, q-Higgs modules, and their cohomology, exploring Frobenius isogeny properties and Nygaard filtration in prismatic F-crystal theory.

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

Systems with Coulomb and Riesz Interactions - 3/3

Explore statistical mechanics of large particle systems with Coulomb/Riesz repulsion through electrostatic analysis, covering equilibrium measures and fluctuations.

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

What is the Universal Scaling Limit of Random Interface Growth and the KPZ Fixed Point - 3/3

Explore the KPZ fixed point and directed landscape as universal limits of random interface growth models, connecting quantum integrable systems to fluctuating hydrodynamics.

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

Introduction to the Physics of the KPZ Universality Class - 3/3

Explore the exactly solvable KPZ universality class, covering scaling properties, distribution functions, and experimental validation of theoretical predictions in statistical physics.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

Locally Homogeneous Flows and Anosov Representations - 5/5

Explore advanced connections between Anosov representations and locally homogeneous flows using modern dynamical systems techniques in Lie group theory.

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

Harmonic Maps in High-Dimensional Spheres, Representations and Random Matrices - 4/4

Explore rigidity phenomena of harmonic maps from 2D surfaces to high-dimensional spheres using random matrix theory and PSL2(R) representation theory in geometric analysis.

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

Geometry of Anosov Flows and Rigidity - 4/4

Explore Anosov flows' geometry, invariant manifolds, and rigidity theorems connecting negatively curved manifolds to constant sectional curvature through advanced dynamical systems.

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

Poisson-Voronoi Tessellations and Fixed Price in Higher Rank - 5/5

Explore Poisson-Voronoi tessellations on symmetric spaces and their application to proving volume-generator relationships in higher rank semisimple Lie groups.

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

Geometry of Anosov Flows and Rigidity - 3/4

Explore Anosov flows' geometry, invariant manifolds, and rigidity results connecting negatively curved manifolds to constant sectional curvature.

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

Poisson-Voronoi Tessellations and Fixed Price in Higher Rank - 4/5

Explore Poisson point processes and ideal Poisson-Voronoi tessellations on symmetric spaces, uncovering connections between manifold volume and fundamental group generators.

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