Institute for Advanced Study Courses

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

Candidate de Sitter Vacua in Type IIB String Theory

Explore type IIB string theory compactifications yielding de Sitter vacua. Examine Calabi-Yau orientifolds, quantized fluxes, and effective supergravity theories in the context of moduli stabilization and metastable vacua.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Reading Alan Turing - Exploring Turing's Influential Ideas in Theoretical Computer Science

Explore Turing's influential papers and their impact on theoretical computer science with Avi Wigderson. Gain insights into Turing's visionary ideas and their modern relevance.

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

Analytic Insights into the Zig-Zag Product and Its Friends - Part I

Explore advanced graph theory with Gil Cohen, delving into the Zig-Zag product and related graph operators using innovative analytic techniques for more precise bounds and insights.

• YouTube
• 1 hour 8 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

Parametrised Whitehead Torsion of Families of Nearby Lagrangians

Explore the parametrised Whitehead torsion as an invariant of manifold families, focusing on its application to exact Lagrangians in cotangent bundles and implications for symplectic mapping class groups.

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

Some Progress on Galaxy-Halo Connection

Explore recent advances in galaxy-halo connection research, including assembly bias detection, neural network modeling, stellar mass-halo mass relation evolution, and innovative halo mass estimation techniques.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

The Quasisymmetric Flag Variety

Delve into the geometric construction of the quasisymmetric flag variety, exploring its cohomology ring, Coxeter Richardson varieties, and the discovery of equivariant quasisymmetry with Graham-positive multiplication structure constants.

• YouTube
• 2 hours 8 minutes
• Self-Paced
• Free Video