Institute for Advanced Study Courses

Elliptic Measures and the Geometry of Domains - Zihui Zhao

Explore elliptic measures and domain geometry with Zihui Zhao. Learn about harmonic measures, uniform domains, and the Piper theorem in this advanced mathematical analysis seminar.

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

Drinfeld's Lemma for Schemes - Kiran Kedlaya

Explore Drinfeld's lemma for schemes with Kiran Kedlaya, covering fundamental groups, base points, and the Stax project in algebraic geometry.

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

Bounds in Renormalized Volume for Hyperbolic 3-Manifolds - Franco Vargas Pallete

Explore advanced geometric concepts in hyperbolic 3-manifolds, focusing on renormalized volume bounds, mean curvature, and variation formulas through rigorous mathematical analysis.

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

A Toy Model of the Information Paradox in Empty Space - Suvrat Raju

Explore the information paradox in empty space through a toy model, examining quantum correlations, Bell inequalities, and their implications for gravity and spacetime structure.

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

Mean Action of Periodic Orbits of Area-Preserving Annulus Diffeomorphisms - Morgan Weiler

Explore area-preserving annulus diffeomorphisms, focusing on mean action of periodic orbits. Delve into action functions, Colombian variants, and Hutchings theorem in symplectic dynamics.

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

Lyapunov Exponents for Small Random Perturbations - Alex Blumenthal

Explore Lyapunov exponents in random perturbations of hyperbolic 2D volume-preserving diffeomorphisms, including the Standard Map, with insights on asymptotic dynamics and invariant structures.

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

X-Ramanujan Graphs - Ex Uno Plures

Explore X-Ramanujan graphs with Ryan O'Donnell, covering additive lifts, generic graphs, eigenvalues, and matching polynomials in this advanced computer science and discrete mathematics seminar.

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

Universality of Random Graphs - Gal Kronenberg

Explore 2-universality in random graphs, covering monotone properties, age universality, probability thresholds, and expansion properties with proof techniques and examples.

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

Notions of Scalar Curvature - Mikhail Gromov

Explore scalar curvature concepts, spin bundles, and rich curves with renowned mathematician Mikhail Gromov in this advanced topology lecture from the Institute for Advanced Study.

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

Existence Theory of Minimal Hypersurfaces - Fernando Marquez

Explore the existence theory of minimal hypersurfaces, covering minimax theorems, space of cycles, and volume spectrum. Gain insights into Ricci curvature and generic metrics.

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

On Voevodsky's Univalence Principle - André Joyal

Explorez le principe d'univalence de Voevodsky avec André Joyal, examinant ses implications pour la théorie des types et les catégories dans cette conférence commémorative approfondie.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Univalence from a Computer Science Point-of-View - Dan Licata

Explore univalence in computer science with Dan Licata, covering Martin-Löf type theory, computation, and applications in homotopy theory and group structures.

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

Univalent Foundations and the Equivalence Principle - Benedikt Ahrens

Explore univalent foundations and the equivalence principle in mathematics, covering type theory, dependent types, and their applications to structures like monoids and categories.

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

Galois, Grothendieck and Voevodsky - George Shabat

Explore the mathematical legacies of Galois, Grothendieck, and Voevodsky, focusing on their contributions to group theory, algebraic geometry, and category theory, with insights into dessins d'enfants and Belyi pairs.

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

Quantum Information and the Black Hole Interior II - Ahmed Almeiri

Explore quantum information's role in black hole interiors, covering key concepts like typicality, central charge, and complementarity in theoretical physics.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video