Institute for Advanced Study Courses

Intensity Interferometry for Sub-Microarcsecond Resolution in AGN Observations

Explore intensity interferometry for sub-microarcsecond resolution in optical telescopes, focusing on applications for active galactic nuclei observations and potential impacts on astrophysics research.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

The Cosmic Quest for Neutrino Mass

Explore the cosmic impact of neutrino mass, from early Universe roles to current experiments. Uncover physical effects, dataset peculiarities, and novel astrophysical probes in the quest to detect relic neutrinos.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Derived Categories of Permutahedral Varieties Through Matroids

Explore derived categories of permutahedral varieties using matroid theory, uncovering connections between algebraic geometry and combinatorics.

• YouTube
• 21 minutes
• On-Demand
• Free Video

The Mysterious Kronecker Coefficients in Algebraic Combinatorics

Explore the enigmatic Kronecker coefficients, their significance in algebraic combinatorics, and recent developments in positivity, asymptotics, and computational complexity.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Characterizations of PAC Learnability

Explore key characterizations of PAC learnability in machine learning theory with insights from postdoctoral researcher Nataly Brukhim.

• YouTube
• 15 minutes
• On-Demand
• Free Video

From Kepler to the Habitable Worlds Observatory: The Emerging Picture of Planet Populations

Explore exoplanet demographics, from Kepler's Earth-like planet discoveries to NASA's Habitable Worlds Observatory, and learn about K2 and TESS's role in expanding our understanding of occurrence rates.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Spectral Gap of the Laplacian for Random Hyperbolic Surfaces - Part 2

Explore spectral gap of Laplacian for random hyperbolic surfaces using trace method and asymptotic expansions in large genus limit. Analyze Weil-Petersson measure and Friedman-Ramanujan property.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Spectral Gap of the Laplacian for Random Hyperbolic Surfaces

Explore spectral gap of Laplacian for random hyperbolic surfaces in large genus limit. Delve into Weil-Petersson measure, Mirzakhani's work, and trace method applications.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Dynamical Formation of Merging Black-Hole Binaries

Explore gravitational wave detection and formation mechanisms of merging compact binaries, including dynamical channels and novel three-body effects. Gain insights into constraining formation theories.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Quantitative Almost-Existence in Dimension Four

Delve into advanced symplectic geometry concepts, exploring Hofer-Zehnder's theorem and the existence of closed characteristics in four-dimensional space through rigorous mathematical analysis.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Sheaves on Graphs, the Hanna Neumann Conjecture, and Algebraic Geometry Applications

Explore advanced graph theory concepts through sheaf theory and the Hanna Neumann conjecture, featuring innovative problem-solving approaches and applications in discrete mathematics.

• YouTube
• 2 hours 6 minutes
• On-Demand
• Free Video

Life on the Edge: Reconnection-Powered Emission at the Boundaries of Black Hole Jets

Explore cutting-edge astrophysics research on emission patterns at black hole jet boundaries and their connection to magnetic reconnection phenomena in space.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Spaces of Lorentzian Polynomials

Delve into advanced mathematical concepts exploring Lorentzian polynomials, their topology, and relationship with local Dressians, featuring insights on compactification and Tutte group connections.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Cohomologically Tropical Varieties and Mixed Hodge Structures

Delve into advanced geometric concepts exploring tropicalizations of torus subvarieties, focusing on Poincaré duality and mixed Hodge structures in relation to hyperplane arrangements.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

The Foundation of a Generalized Parallel Connection

Delve into advanced matroid theory, exploring foundations, generalized parallel connections, and their relationship with tensor products in algebraic geometry and representation theory.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video