Institute for Advanced Study Courses

Recent Progress on Mean Curvature Flow

Delve into recent mathematical breakthroughs in mean curvature flow theory, including solutions to longstanding conjectures and insights into singularity formation in evolving surfaces.

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

Chow Functions for Partially Ordered Sets

Delve into advanced mathematical concepts of Chow functions and their applications in KLS theory, exploring relationships between combinatorial structures and cohomological aspects.

• YouTube
• 1 hour 45 minutes
• Self-Paced
• Free Video

Singular Points on Positroid Varieties and Physics Applications

Delve into positroid varieties, their singularity criteria, and connections to physics through affine pipe dreams and plabic diagrams, with applications to BCFW bridge decomposition.

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

Contact Topology Meets Thermodynamics

Explore the intersection of contact topology and thermodynamics, examining equilibrium concepts through advanced mathematical perspectives and their applications in physics.

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

Problems in Extremal Combinatorics and Connections with Multiparty Communication Complexity

Delve into advanced concepts in extremal combinatorics and multiparty communication complexity, exploring connections between fields and recent developments in the Corners Problem and 3AP problem.

• YouTube
• 2 hours 7 minutes
• Self-Paced
• Free Video

Quantum Cosmology in 2+1 Dimensions

Delve into quantum cosmology models in 2+1 dimensions, exploring solvable scenarios with negative and positive cosmological constants, static patch Hamiltonians, and their relationship to CFT observables.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Quantum Steenrod Operations, p-curvature, and Representation Theory

Delve into advanced mathematical concepts connecting quantum Steenrod operations, p-curvature, and 3D mirror symmetry in symplectic geometry, with applications to representation theory.

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

Bounding Lagrangian Intersections Using Floer Homotopy Theory

Delve into advanced mathematical concepts exploring Lagrangian intersections through Floer homotopy theory, featuring new lower bound calculations and Steenrod squares applications in symplectic geometry.

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

Systolic Inequalities for S1-invariant Contact Forms in Three-Dimensional Geometry

Delve into advanced contact geometry concepts, focusing on systolic inequalities and their relationship with S1-invariant contact forms in three-dimensional manifolds.

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

Selmer Groups and Hilbert's Tenth Problem

Explore Selmer groups as cohomological tools for solving diophantine equations, with applications to Hilbert's tenth problem over finitely generated rings.

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

Improved Private Information Retrieval Schemes from Matching Vectors and Derivatives

Delve into Private Information Retrieval (PIR) schemes, exploring improved methods for secure database access using matching vectors and derivatives, with significant communication efficiency improvements.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Duality of Decaying Turbulence to a Solvable String Theory

Delve into the mathematical reformulation of Navier-Stokes equations as a solvable string theory, exploring how the Euler ensemble provides analytical solutions for decaying turbulence phenomena.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

Trust and Distrust in ML: Privacy, Verification and Robustness - Part 2

Delve into privacy, verification, and robustness challenges in machine learning with Shafi Goldwasser's exploration of trust issues in ML systems.

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

Legendrian Non-Squeezing via Microsheaves

Delve into quantitative embedding results for Legendrian submanifolds, exploring contact non-squeezing theorems and microsheaves with applications to monotone Lagrangian tori in ℂn.

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

Using Logic to Investigate Homeomorphism Groups of Manifolds

Delve into the application of logic and descriptive set theory to understand countable groups acting on manifolds, extending beyond classical characterizations of homeomorphism groups.

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