Centre de recherches mathématiques - CRM Courses

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

Divisibility of Spheres with Measurable Pieces - Oleg Pikhurko

Explore divisibility of spheres with measurable pieces, focusing on Euclidean (d-1)-dimensional sphere S^(d-1) and special orthogonal matrices. Examine impossibility of measurable divisibility for generic rotations.

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

Non-Almost Finite Actions on the Cantor Set - Amenable Wreath Products

Explore non-almost finite actions on the Cantor set by amenable wreath products, challenging Kerr's topological analogue of the Ornstein-Weiss theorem in measurable dynamics.

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

A Substitute for Kazhdan's Property (T) for Universal Non-Lattices - Lecture

Explore computer-assisted methods for proving property (T) in geometric group theory, including recent developments and human efforts to understand these proofs.

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

A Borel Local Lemma for Finite Asymptotic Separation Index

Explore a Borel version of the Lovász Local Lemma for graphs with finite asymptotic separation index, improving measurable local lemma exponents and extending to exponential growth groups.

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

IRS of Non-Archimedean Groups - Measured Group Theory

Explorez les IRS des groupes non archimédiens, en élargissant la définition aux groupes polonais et en examinant les sous-groupes fermés du groupe de permutation de N.

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

Measure Equivalence and Wreath Products in Group Theory

Explore measure equivalence and wreath products in group theory, focusing on nonabelian free groups and orbit equivalence of wreath products.

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

Stationary Random Subgroups and Injectivity Radius in Negative Curvature

Explore stationary random subgroups and injectivity radius in negative curvature, focusing on rank one simple Lie groups and hyperbolic manifolds. Gain insights into recent theorems and their applications.

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

Fixed Price One for Higher Rank Groups - Measured Group Theory

Explore proof techniques for fixed price one in higher rank groups, with applications to lattices. No prior Lie theory knowledge required.

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