Institut des Hautes Etudes Scientifiques (IHES) Courses

Locally Homogeneous Flows and Anosov Representations - 4/5

Explore advanced techniques connecting Anosov representations to locally homogeneous flows with uniformly hyperbolic dynamics, bridging Lie theory and smooth dynamical systems.

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

Poisson-Voronoi Tessellations and Fixed Price in Higher Rank - 3/5

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

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

Harmonic Maps in High-Dimensional Spheres, Representations and Random Matrices - 2/4

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

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

Locally Homogeneous Flows and Anosov Representations - 3/5

Explore advanced mathematical concepts connecting Anosov representations with locally homogeneous flows, featuring modern analytic techniques from smooth dynamics and differential geometry.

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

Geometry of Anosov Flows and Rigidity - 2/4

Explore Anosov flows through geodesic dynamics on negatively curved manifolds, covering invariant manifolds, ergodicity, and rigidity results for totally geodesic hypersurfaces.

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

Locally Homogeneous Flows and Anosov Representations - 2/5

Explore advanced mathematical concepts connecting Anosov representations with locally homogeneous flows, featuring modern analytic techniques from smooth dynamics and differential geometry.

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

Measure Rigidity in Higher Rank Lattice Actions - 3/3

Explore measure rigidity in higher rank lattice actions, covering Margulis' theorems and recent developments in the Zimmer program for smooth manifold actions.

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

Poisson-Voronoi Tessellations and Fixed Price in Higher Rank - 1/5

Explore Poisson point processes and Poisson-Voronoi tessellations on symmetric spaces, connecting geometric properties to fundamental group generators in higher rank Lie groups.

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

Locally Homogeneous Flows and Anosov Representations - 1/5

Explore Anosov representations through locally homogeneous flows, connecting hyperbolic dynamics with semi-simple Lie groups and modern analytic techniques in smooth dynamics.

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

Higher Property T

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 - 4/4

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

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

Measure Rigidity in Higher Rank Lattice Actions - 2/3

Explore measure rigidity in higher rank lattice actions, covering Margulis' theorems and recent developments in the Zimmer program for smooth manifold actions.

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

The Geometry of Diverging Orbits - 2/3

Explore diagonal group actions on homogeneous spaces that escape to infinity, using representation theory and geometric properties to analyze their structure and distinguish orbit types.

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

Thermodynamical Formalism and Geometric Applications - 3/3

Explore thermodynamical formalism and Gibbs measures for hyperbolic surface geodesic flows, with applications to entropy regularity and horocyclic flow analysis.

• YouTube
• 1 hour 13 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 6 minutes
• Self-Paced
• Free Video