Institute for Advanced Study Courses

Quantitative Contact Big Fiber Theorem

Delve into the proof of contact big fiber theorem using contact Hamiltonian Floer homology, exploring non-displaceable fibers in Liouville fillable contact manifolds and partial contact quasi-state concepts.

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

Locally Testable Codes with the Multiplication Property from High-dimensional Expanders

Explore the construction of locally testable codes with multiplication property using high-dimensional expanders, addressing a key open question in error-correcting codes and proof systems.

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

Opportunities and Challenges for Indexing a Polyglot Society: The Development of HIMME

Explore the challenges and opportunities of using digital methods to study multilingual medieval Middle Eastern societies through the development of HIMME (Historical Index of the Medieval Middle East).

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

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

Reeb Orbits Frequently Intersecting a Symplectic Surface

Delve into advanced symplectic geometry concepts, exploring Reeb orbits' interactions with symplectic surfaces and their implications for area-preserving surface diffeomorphisms.

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

Random Matrices From GLn(q) Sampled by Words in Free Groups

Explore the fascinating relationship between word-distributions in matrix groups over finite fields and free group algebras, examining connections with symmetric group distributions and key conjectures.

• YouTube
• 2 hours 10 minutes
• Self-Paced
• Free Video

New Tensor Categories - Work on Pretannakian Categories and Linear Algebraic Groups

Delve into advanced tensor categories and pretannakian theory, exploring groundbreaking developments in representation theory and algebraic groups through recent mathematical discoveries.

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

Structure and Randomness for Finite-field Polynomials are Almost Equivalent

Delve into polynomial equations over finite fields, exploring their solutions, derivatives, and connections to number theory and coding theory through new combinatorial approaches to tensor rank.

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

Local-to-Global Theorems on High Dimensional Expanders

Explore high dimensional expansion theory, from graph fundamentals to complex applications in error-correcting codes and PCPs, focusing on how local properties influence global behaviors in mathematical structures.

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

Quantum Locally Testable Codes and Codes with Transversal Gates

Delve into advanced quantum error correction concepts, focusing on qLDPC codes, local testability, and transversal gates through higher-dimensional construction methods and cup product structures.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video