Institute for Advanced Study Courses

The Realization Space of a Matroid

Explore the intricacies of matroid realization spaces with Lukas Kühne, delving into advanced mathematical concepts and their applications in combinatorial geometry.

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

Stability Problems in General Relativity

Explore stability problems in general relativity, focusing on mathematical challenges and recent advancements in understanding gravitational phenomena.

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

Insights and Challenges in Symplectic Capacities

Explore key insights and challenges in symplectic capacities, delving into advanced mathematical concepts and their applications in geometric analysis.

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

Total Positivity and Determinantal Inequalities

Explore total positivity and determinantal inequalities in mathematics, focusing on advanced concepts and their applications in various fields.

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

Insights into the Geometric Harmonic Analysis Associated to 1-Parameter Sets

Explore geometric harmonic analysis of 1-parameter sets with insights from D. Dominique Kemp's research at the Institute for Advanced Study.

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

Sorting Using Partial Information - Lecture

Explore efficient sorting algorithms using partial information, combining topological sort and heapsort techniques to achieve optimal time and comparison bounds for binary comparisons.

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

Determinants of Cohomology for Number Fields

Explore determinants of cohomology in number fields, delving into advanced mathematical concepts and their applications in algebraic number theory.

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

Quasipolynomial Bounds for Some Problems in Extremal Combinatorics

Explore quasipolynomial bounds in extremal combinatorics with Zander Kelley, examining key problems and recent advancements in this mathematical field.

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

Homotopy Rigidity of Nearby Lagrangian Fibers

Explore homotopy rigidity of nearby Lagrangian fibers in this advanced mathematical talk by Yash Deshmukh, delving into complex geometric structures and topological relationships.

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

Top Heaviness in Combinatorics and Geometry

Explore top heaviness in combinatorics and geometry, examining its applications and implications in mathematical research.

• YouTube
• 19 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