Centre de recherches mathématiques - CRM Courses

Inequalities Between Neumann and Dirichlet Laplacian Eigenvalues on Planar Domains

Explore inequalities between Neumann and Dirichlet Laplacian eigenvalues on planar domains, generalizing Payne's theorem to simply connected Lipschitz domains using novel variational principles.

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

Geometric Stability of Weyl's Law and Applications to Asymptotic Spectral Shape Optimization

Explore geometric stability of Weyl's law and its applications to asymptotic spectral shape optimization, focusing on eigenvalue behavior in bounded Lipschitz domains.

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

On Strong Solutions of Time Inhomogeneous Itô's Equations with Morrey Diffusion Gradient and Drift - CSMQ Colloquium

Explore strong solutions of time-dependent Itô's equations with irregular diffusion and drift terms in Morrey spaces, including existence, uniqueness, and related parabolic equations.

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

On the Spectrum of the Poincaré Operator in Ellipsoids

Explore the Poincaré operator's spectrum in ellipsoids, examining fluid motion, wave operators, and eigenvalue asymptotics in rotating incompressible fluids.

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

The Classification of Finite-Dimensional Lie Algebras of Hamiltonian Vector Fields on the Plane

Explore finite-dimensional Lie algebras of Hamiltonian vector fields on the plane, their classification, properties, and applications in studying Hamiltonian systems.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Complex Analysis, Thick Sets, and Spectral Inequalities

Explorez l'analyse complexe, les ensembles épais et les inégalités spectrales appliqués à la théorie du contrôle et à la géométrie spectrale. Découvrez des techniques analytiques complexes pour les domaines et opérateurs.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

One-ended Spanning Trees in Amenable Group Actions

Explore one-ended spanning trees in free Borel actions of amenable groups, with applications to Borel combinatorics. Discover related results in Baire measurable and Borel settings.

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

Component Finite Subgraphs of Treeings

Explore upper and lower bounds on measurable component finite subgraphs of regular treeings, with focus on hyperfinite subgraphs and probabilistic combinatorics.

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

A Quantitative Neumann Lemma for Finitely Generated Groups - Measured Group Theory

Explore coset covering functions in infinite, finitely generated groups. Discover lower bounds, linear growth in amenable groups, and exponential behavior in property (T) groups.

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

Poisson Boundaries Without Moment Conditions for Hyperbolic Groups

Explore advanced techniques for identifying Poisson boundaries of hyperbolic groups, focusing on the innovative "pin down approximation criterion" for finite entropy measures without moment assumptions.

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

Compact IRS and Compact URS in Group Theory

Explore generalizations of normal subgroups through Invariant Random Subgroups and Uniformly Recurrent Subgroups. Examine their behavior and recent findings on compact IRS and URS.

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

Unimodular Galton-Watson Treeings and Irregular Random Graphs - Almost Ramanujan

Explore spectral radii in graph limit theory, focusing on Unimodular Galton-Watson trees and irregular random graphs. Discover insights into the relationship between local and global graph properties.

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

Realizations of Equivalence Relations and Subshifts

Explore countable Borel equivalence relations, continuous actions on compact spaces, and subshifts. Investigate complexity and genericity of properties like hyperfiniteness in the space of subshifts.

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

L1 Full Groups of Flows in Measured Group Theory

Explore probability measure-preserving actions of reals, associated Polish groups, and their properties. Investigate L1 full groups, their abelianization, and topological rank.

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

Connes-Weiss and Glasner-Weiss Theorems for Kazhdan Equivalence Relations and Cost - Lecture

Explore Connes-Weiss & Glasner-Weiss theorems for Kazhdan equivalence relations, extending to measured equivalence relations and simplifying proofs for groupoid cost.

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