Institut des Hautes Etudes Scientifiques (IHES) Courses

An Introduction to Higher Rank Teichmüller Theory - 3/4

Explore discrete subgroups of semisimple Lie groups and their deformation theory through character varieties, Anosov conditions, and Θ-positivity frameworks.

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

The Geometry of Diverging Orbits - 1/3

Explore diagonal group actions on homogeneous spaces and their escape to infinity, using representation theory and geometric properties to analyze orbit structures in modern dynamics.

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

Measure Rigidity in Higher Rank Lattice Actions - 1/3

Explore measure rigidity in higher rank lattice actions, covering definitions, properties, and applications to Margulis' theorems and the Zimmer program.

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

An Introduction to Higher Rank Teichmüller Theory - 2/4

Explore discrete subgroups of semisimple Lie groups and their deformation theory through character varieties, focusing on Anosov conditions and Θ-positivity frameworks.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Higher Property T - Kazhdan's Property and Group Cohomology

Explore advanced group theory through Kazhdan's Property T and its higher-degree generalizations, covering Garland's results, Lie groups, lattices, and applications.

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

Thermodynamical Formalism and Geometric Applications - 2/3

Explore thermodynamical formalism through Gibbs measures for hyperbolic surface geodesic flows and their applications to geometric problems like entropy regularity.

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

Higher Property T - 2/5

Explore advanced group theory through Kazhdan's Property T and its higher-degree generalizations, covering Garland's results, Lie groups, lattices, and applications.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

An Introduction to Higher Rank Teichmüller Theory - 1/4

Explore discrete subgroups of semisimple Lie groups and their deformation theory through character varieties, focusing on Anosov conditions and Θ-positivity frameworks.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Thermodynamical Formalism and Geometric Applications - 1/3

Discover thermodynamical formalism through Gibbs measures for geodesic flows on hyperbolic surfaces, exploring their ergodic properties and geometric applications.

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

Higher Property T - 1/5

Explore Kazhdan's Property T and its higher degree generalizations, covering Garland's results, Lie groups, lattices, and applications in this advanced mathematical analysis.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Small Scale Index Theory, Scalar Curvature, and Gromov's Simplicial Norm

Explore how scalar curvature constrains manifold topology through small scale index theory and Gromov's simplicial norm in this advanced mathematical research talk.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

3-Manifolds with Positive Scalar Curvature and Bounded Geometry

Discover groundbreaking results on 3-manifolds with positive scalar curvature and bounded geometry, proving contractible cases must be R³ and exploring handlebody constraints.

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

Union of Tubes and Kakeya Sets - 2/3

Explore advanced techniques like Cordoba argument and projection theory to prove volume bounds on tube unions in R2 and R3, with key applications to the challenging Kakeya problem.

• YouTube
• 2 hours 46 minutes
• Self-Paced
• Free Video

Union of Tubes and Kakeya Sets - 1/3

Discover advanced techniques like Cordoba argument and projection theory to prove volume bounds on tube unions in R2 and R3, with key applications to the challenging Kakeya problem.

• YouTube
• 2 hours 10 minutes
• Self-Paced
• Free Video

Union of Tubes and Kakeya Sets - 3/3

Explore advanced techniques like Cordoba argument and projection theory to prove volume bounds on tube unions in R² and R³, with applications to the challenging Kakeya problem.

• YouTube
• 2 hours 40 minutes
• Self-Paced
• Free Video