Institute for Advanced Study Courses

Floer Homology with DG Coefficients - Applications to Cotangent Bundles

Explore Floer homology with DG coefficients and its applications to cotangent bundles. Gain insights into symplectic geometry and dynamical systems through advanced mathematical concepts.

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

Non-escape of Mass for Arithmetic Quantum Limits on Hyperbolic 4-Manifolds

Explore non-escape of mass for Hecke-Maass cusp forms on hyperbolic 4-manifolds, addressing challenges in unbounded Hecke relations and utilizing quaternionic matrices for unique factorization.

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

A Mathematical Vocabulary for Textures and its Astronomical Applications

Explore mathematical approaches to texture analysis and their applications in astronomy, focusing on innovative techniques for cosmic structure interpretation.

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

Entanglement Implications of the Python's Lunch Conjecture

Explore quantum entanglement implications of the Python's Lunch Conjecture in black holes, presented by Alex May from Perimeter Institute at IAS.

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

Second Moment of the GL_3 Standard L-function on the Critical Line

Explore advanced number theory concepts, focusing on GL_3 L-functions, moments of the Riemann zeta function, and applications to the Rankin-Selberg problem.

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

Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties

Explore higher dimensional Fourier quasicrystals and their connection to Lee-Yang varieties. Delve into multidimensional crystalline measures, stable polynomials, and complex algebraic geometry.

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

Combinatorial Inequalities and Combinatorial Interpretations - Part II

Explore polynomial inequalities and their combinatorial interpretations, focusing on defect analysis and algebraic representations in this advanced seminar on combinatorial mathematics.

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

Subgroup Tests and Tailored Non-local Games - Lecture on Interactive Proof Systems

Explore advanced concepts in interactive proof systems, refuting the Aldous-Lyons conjecture through subgroup tests and tailored non-local games.

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

Imagining Other Worlds: How Planet-Forming Disks Can Shed Light on What Is Possible

Explore planet-forming disks and their role in shaping potential exoplanets, gaining insights into the diversity of planetary systems in our galaxy.

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

Hodge Theory for Non-Archimedean Analytic Spaces

Explore Hodge theory for non-Archimedean analytic spaces, extending Deligne's work and generalizing complex analytic constructions. Gain insights into K-analytic spaces and their cohomology groups.

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

Combinatorial Inequalities and Combinatorial Interpretations - Part I

Explore classical inequalities in enumerative and algebraic combinatorics, their combinatorial interpretations, and their impact on the field. Gain insights into complexity theoretic aspects.

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

Subgroup Tests and the Aldous-Lyons Conjecture

Explore the refutation of the Aldous-Lyons conjecture through novel interactive proof systems and subgroup tests, connecting complexity theory to probability theory and group theory.

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

Introduction to Chern Simons Theory and Topology

Explore Chern Simons Theory and its connections to topology with renowned physicist Edward Witten in this advanced workshop on quantum information and physics.

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

Experimental Implementations of Quantum Computers and Simulations

Explore cutting-edge quantum computing implementations and simulations with insights from a leading expert in quantum optics and information theory.

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

Discussion on MIP* = RE

Explore the groundbreaking MIP* = RE theorem with MIT's Anand Natarajan, delving into its implications for quantum computing, complexity theory, and the foundations of mathematics.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video