Spectral Gap Courses and Certifications

Hausdorff Center for Mathematics

Dynamics - Topology and Numbers

Explore advanced mathematical dynamics through expert lectures on homogeneous dynamics, transfer operators, quantum modular forms, and spectral theory applications.

• YouTube
• 1 day 4 hours 54 minutes
• On-Demand
• Free Video

Banach Center

Spectral Gaps vs the Baum-Connes Conjecture

Explore the relationship between spectral gaps and the Baum-Connes conjecture in mathematics, delving into advanced concepts in functional analysis and topology.

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

ICTP Mathematics

Dynamics of Smooth Surface Diffeomorphisms - Spectral Gap and Stochastic Properties

Explore surface diffeomorphisms, spectral gaps, and stochastic properties in smooth dynamics. Gain insights into symbolic models, entropy continuity, and hyperbolic systems.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Towards an Optimal Spectral Gap Result for Random Compact Hyperbolic Surfaces

Explore recent progress in proving near-optimal spectral gaps for hyperbolic surfaces. Delve into trace methods, challenges, and new tools developed to improve bounds in spectral geometry.

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

Institute for Advanced Study

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

Institute for Advanced Study

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

Institut Henri Poincaré

On the Spectral Gap of the Laplacian for Random Hyperbolic Surfaces

Explorez le comportement spectral du laplacien sur des surfaces hyperboliques aléatoires, en mettant l'accent sur l'écart spectral dans la limite des grands genres.

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

Simons Semester on Dynamics

A Spectral Gap for the Transfer Operator on Complex Projective Spaces - Lecture 4

Explore the transfer operator on complex projective spaces, focusing on spectral gaps, equilibrium states, and statistical properties in holomorphic dynamics. Gain insights into pluripotential theory applications.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Spectral Gap Estimates for the Random Field Ising Model - Lecture

Spectral gap estimates for random field Ising model: convergence rates, Glauber dynamics, Griffiths phase. Combines stochastic localization and percolation-theoretic coarse-graining techniques.

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

Institute for Advanced Study

Strong Spectral Gap for Geometrically Finite Hyperbolic Manifolds

Discover new results establishing strong spectral gap for geometrically finite hyperbolic manifolds with critical exponent greater than (n−1)/2, settling a 2015 conjecture.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Spectral Gap for Random Schottky Surfaces

Delve into advanced mathematical concepts exploring spectral gaps in random Schottky surfaces, examining the behavior of Laplace eigenvalues and their relationship to hyperbolic geometry and probability theory.

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

Institute for Advanced Study

Analysis and Mathematical Physics

Explore advanced mathematical physics through expert lectures on quantum systems, fluid dynamics, spectral theory, geometric analysis, and cutting-edge research from leading mathematicians and physicists.

• YouTube
• 3 days 8 hours 42 minutes
• On-Demand
• Free Video

Institut Henri Poincaré

Random Walks and Asymptotic Geometry of Groups

Explore advanced mathematical concepts connecting random walks with asymptotic geometry of groups through expert lectures from leading researchers in the field.

• YouTube
• 16 hours 47 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Kinetic Theory - Junior Trimester Program

Explore advanced mathematical theories in kinetic equations, particle systems, and their applications through expert lectures on diffusion, equilibrium, and scaling limits.

• YouTube
• 2 days 18 hours 50 minutes
• On-Demand
• Free Video

Random Walks on Finite Groups, Part 2 - Lecture 18

Explore Selberg's random walk estimate through the Sarnak-Xue approach in this advanced projection theory lecture covering finite group probability distributions.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video