Institute for Advanced Study Courses

All-Pairs Min-Cut vs. All-Pairs Shortest-Path

Explore groundbreaking algorithms that break the 60-year cubic barrier for All-Pairs Min-Cut, revealing surprising separations from shortest-path problems using expander decompositions.

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

Studying 3D CFTs with the Fuzzy Sphere - Chern-Simons-Matter Theories and Fermionic CFTs

Explore 3D conformal field theories using fuzzy sphere methods, focusing on Chern-Simons-matter theories, quantum Hall physics connections, and fermionic CFTs with experimental applications.

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

Tropical Wave-Fronts and Nodal Tangles

Explore tropical geometry applications to symplectic 4-manifolds and toric fibrations, examining moduli spaces and connectivity through advanced mathematical techniques.

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

Open Gromov-Witten Invariants for Even-Dimensional Lagrangians

Explore genus zero open Gromov-Witten invariants for even-dimensional Lagrangians using canonical bounding cochains with non-commutative coefficients and quadric computations.

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

Equidistribution of Expanding Horospheres in the Space of Translation Surfaces

Explore equidistribution of expanding horospheres in translation surfaces, proving Forni's conjecture and extending Eskin-Mirzakhani results with applications to rational angle billiards.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Typical and Atypical Intersections - Geometry, Dynamics, and Applications

Explore geometric spaces and their special submanifolds through unlikely intersections, covering complex hyperbolic lattices and the Hodge locus distribution.

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

Are We There Yet? First-Principles Modeling of Multimessenger Signals in the Plasma Universe

Explore first-principles modeling of black hole plasma environments and their multimessenger signals through advanced magnetohydrodynamic and kinetic simulations.

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

When is the Geodesic Flow Ergodic?

Explore the connection between geodesic flow ergodicity and Brownian motion recurrence on infinite Riemann surfaces, with new results on Fenchel-Nielsen parameters.

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

Estimates for Ricci Solitons in Dimension 4

Explore advanced estimates for Ricci solitons in 4D geometry, covering self-similar solutions to Ricci flow and their role in modeling singularity formation.

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

Symplectic Rigidity of Anosov Flows Under Orbit Equivalence

Explore how orbit equivalent Anosov flows preserve symplectic invariants through Liouville structures, revealing deep connections between dynamics and symplectic geometry.

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

On Turán Numbers of Hypergraphs

Explore extremal combinatorics through Turán numbers of hypergraphs, covering fundamental techniques and recent results on tight cycles with novel coloring characterizations.

• YouTube
• 2 hours 9 minutes
• Self-Paced
• Free Video

Entanglement Bootstrap and Conformal Field Theory

Explore quantum many-body states through entanglement bootstrap methods to understand conformal field theory and extract universal data from local entanglement information.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Frobenius Lifting and a Geometric Theory of Companion Forms

Explore Frobenius lifting obstructions on Shimura varieties and their applications to companion forms theory in classical modular forms and higher dimensions.

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

New Methods in Resolution of Singularities

Explore groundbreaking advances in resolution of singularities, from Hironaka's 1964 method to the revolutionary "dream algorithm" discovered in 2019 using weighted stack-theoretic techniques.

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

Trickle-down Theorems for High-dimensional Expanders via Lorentzian Polynomials

Explore trickle-down theorems for high-dimensional expanders using Lorentzian polynomials, with applications to coding theory, PCPs, pseudorandomness, and approximate sampling.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video