Institut des Hautes Etudes Scientifiques (IHES) Courses

Logarithmic Sobolev Inequalities on Homogeneous Spaces

Explore logarithmic Sobolev inequalities on homogeneous spaces with sub-Riemannian structures. Discover how constants depend on Lie group geometry and remain independent of dimension in certain cases.

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

Dimension-Independent Functional Inequalities on Sub-Riemannian Manifolds

Explore gradient estimates and functional inequalities on sub-Riemannian manifolds, focusing on techniques used in absence of curvature bounds. Learn basics of sub-Riemannian geometry and metric structures.

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

Quantum Periods for Complements

Explore quantum periods for complements, focusing on polynomial-defined spectral curves and quantization of polynomial algebras. Gain insights into cohomological descriptions of WKB series.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Topological Invariants of Gapped States and 't Hooft Anomalies

Explore topological invariants of gapped ground-states in lattice systems, their interpretation as obstructions to gauging, and the role of locality in infinite-volume systems with rapidly decaying interactions.

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

Modularity of Donaldson-Thomas Invariants on Calabi-Yau Threefolds

Explore Donaldson-Thomas invariants, their mathematical significance, and modular behavior in string theory. Gain insights into BPS indices, wall-crossing phenomena, and topological string amplitudes.

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

Inclusive Scattering Matrix in Quantum Theory

Explore inclusive scattering matrix in quantum theory, its relation to cross-sections, and applications in quantum electrodynamics using geometric approach and Keldysh formalism.

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

Prime, Knots and the Adele Class Space

Explore geometric connections between primes and knots through scaling site theory, adele class space, and finite abelian extensions of Q, revealing insights into number theory and topology.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Topological Recursion: A Recursive Way of Counting Surfaces

Explore topological recursion for enumerating surfaces in combinatorics, geometry, and physics. Learn how this universal method links to integrable systems and random matrices.

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

Quantum Exclusion Process, Random Matrices and Free Cumulants

Explore quantum exclusion process, random matrices, and free cumulants in relation to particle hopping models and their invariant measure fluctuations.

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

Matrix Model for Structure Constants of Huge Protected Operators in N=4 SYM Theory

Explore matrix model representations for protected correlation functions of huge operators in N=4 SYM theory, unveiling connections to integrable hydrodynamics and Calogero-Moser models.

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

Entangleability of Cones

Explore tensor products of finite-dimensional proper cones, solving Barker's conjecture using convex geometry and algebraic topology, with applications to entanglement in non-classical systems.

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

Waists Measured via Urysohn Width in Riemannian Manifolds

Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.

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

Width, Scalar Curvature and Macroscopic Scalar Curvature

Explore the interplay between positive scalar curvature and macroscopic scalar curvature, examining Urysohn width and closed geodesics in PSC and PMSC spaces.

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

Spectra of Laplace and Dirac Operators on Noncompact Manifolds

Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.

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

On the L^p Spectrum of the Laplacian on Riemannian Manifolds

Explore the $L^p$ spectrum of the Laplacian on manifolds, including resolvent sets, Weyl criterion, and hyperbolic space, with insights on conformally compact manifolds.

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