Institute for Advanced Study Courses

Lengths of Closed Geodesics in Manifolds of Positive Scalar Curvature

Explore Gromov's conjecture proof on short closed geodesics in 3-manifolds with positive scalar curvature using Min-Max theory and minimal surfaces techniques.

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

Obfuscation is a Wheelbarrow - How to Build Long-Sought Cryptography Using Complexity Theory

Discover how complexity theory enables breakthrough cryptographic constructions, including optimal public-key encryption, through innovative circuit obfuscation techniques.

• YouTube
• 2 hours 1 minute
• Self-Paced
• Free Video

Mathematical Exploration and Discovery at Scale

Discover how AlphaEvolve uses AI to autonomously tackle mathematical problems across analysis, geometry, combinatorics, and number theory, revolutionizing discovery at unprecedented scale.

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

How Low Can We Go? Exploring Minimal Assumptions in Quantum Cryptography

Explore minimal assumptions needed for secure quantum cryptography protocols, covering encryption, signatures, and quantum money without requiring prior quantum knowledge.

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

Subleading Asymptotics of ECH Capacities and Symplectic Packing Problems

Explore subleading asymptotics of ECH capacities in toric domains and their connection to symplectic packing problems, with applications to packing stability failures.

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

Continuation Maps for the Morse Fundamental Group

Explore continuation maps for Morse fundamental groups and their functoriality properties in symplectic topology through combinatorial recovery of fundamental groups from Morse-Smale pairs.

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

Equivariant Lagrangian Non-Displacements

Explore ℤ2-equivariant Floer cohomology to detect non-displaceability of Lagrangian submanifolds under group actions, focusing on S¹-invariant Lagrangians in ℂⁿ using Floer-Euler classes.

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

On the Hilbert Space of Quantum Gravity from the Gravitational Path Integral

Explore quantum gravity's Hilbert space through gravitational path integrals, examining positivity criteria for open/closed universes and transition probabilities with non-perturbative corrections.

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

Emergent Mixed States for Baby Universes and Black Holes

Explore quantum states in AdS/CFT correspondence, examining how black holes and baby universes lead to mixed states rather than pure ones in the semiclassical limit.

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

Filtering CFTs at Large N - Euclidean Wormholes, Closed Universes, and Black Hole Interiors

Explore advanced theoretical physics concepts linking Euclidean wormholes, closed universes, and black hole interiors through large-N conformal field theory filtering procedures.

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

Near-Extremal Black Hole Evaporation

Explore the quantum mechanics of near-extremal black hole evaporation and its implications for spacetime physics in this advanced theoretical physics workshop.

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

Observers, Alpha Parameters, and the Hartle-Hawking State - Part II

Explore quantum aspects of black holes through the Hartle-Hawking state, examining closed universe physics and classical observers in holographic theories with spherical topology.

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

A Black Hole Airy Tail - Part 2

Explore quantum black hole entropy puzzles in JT gravity, uncovering how semi-quenched methods and matrix models resolve negative entropy issues through Airy statistics and wormhole effects.

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

A Black Hole Airy Tail - Part 1

Explore quantum gravity's entropic puzzles in JT gravity, uncovering how non-perturbative effects and Airy distributions resolve negative entropy at low temperatures.

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

Strong Spectral Gap for Geometrically Finite Hyperbolic Manifolds

Discover new results establishing strong spectral gap for geometrically finite hyperbolic manifolds with critical exponent greater than (n−1)/2, settling a 2015 conjecture.

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