Centre de recherches mathématiques - CRM Courses

Finitely Generated Normal Subgroups of RAAGs

Explore finitely generated normal subgroups of Right-Angled Artin Groups (RAAGs) in this mathematical deep dive into CAT(0) cube complexes.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Effective Rank-Rigidity in CAT(0) Cube Complexes

Explore CAT(0) cube complexes and rank-rigidity, examining uniform flipping and skewering techniques to determine group actions and geometric properties.

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

Helly Graphs and Injective Metric Spaces - Part 3

Explorez les graphes de Helly et les espaces métriques injectifs, leurs propriétés et constructions, en mettant l'accent sur les caractéristiques non positives et les applications géométriques.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

An Invitation to the Lifting Decomposition in CAT(0) Cube Complexes

Explorez la décomposition de levage dans les complexes cubiques CAT(0), ses applications et connexions avec diverses frontières, offrant de nouvelles perspectives en géométrie combinatoire.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Median Spaces and Algebras - Part 3

Explore median spaces as generalizations of L^1 spaces, CAT(0) cube complexes, and R-trees. Discover their applications in geometric group theory and functional analysis.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Ascending Chains of Free Groups in 3-Manifold Groups

Explore ascending chains of free groups in 3-manifold groups, examining proofs and techniques involving hyperbolic geometry, geometrization, and JSJ decompositions.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Dense Embeddings of Hyperbolic Manifold Groups

Explore dense embeddings of hyperbolic manifold groups, focusing on amalgamated products and linear Lie groups. Learn strategies to control properties of output embeddings.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Geometrization and its Consequences in 3-Manifold Topology - Lecture 4

Explore hyperbolic geometry's role in 3-manifold topology, including Thurston's viewpoint and Perelman's theorem. Discover algorithmic and group-theoretic applications in computational experiments.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Profinite Properties of Finite-Volume Hyperbolic 3-Manifold Groups

Explore profinite rigidity of finite-volume hyperbolic 3-manifold groups, examining volume, invariant trace fields, and arithmeticity as profinite invariants in geometric topology.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

A Combinatorial Characterization of Geometric 3-Manifolds - Lecture

Explore geometric 3-manifolds through combinatorial characterization, focusing on Thurston geometries and their local combinatorial definitions. Learn about new algorithms for geometric decomposition.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

3-Manifold Groups and Fundamental Group Conjectures - Part II

Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte, en examinant les conjectures de Cannon et Wall et leurs interconnexions.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Notions of Nonpositive Curvature and Groups - Lecture 2

Explorez les théories de petite simplification et leurs liens avec les complexes systoliques et quadriques. Découvrez comment ces espaces combinatoires à courbure non positive s'appliquent à l'étude des groupes.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Median Spaces and Algebras - Part I

Explorez les espaces médians et leurs applications en géométrie de groupe, couvrant les espaces L^1, les complexes cubiques CAT(0) et les R-arbres, avec des implications pour diverses propriétés de groupe.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Virtually Free-by-Cyclic Groups

Explore recognition methods for virtually free-by-cyclic groups within hyperbolic compact special groups using homology techniques.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Subgroup Separability of 3-Manifold Groups and Its Applications

Explore subgroup separability in 3-manifold groups, its characterization via torus decomposition, and applications to subgroup distortion and Grothendieck rigidity. Joint work with Hoang Thanh Nguye.

• YouTube
• 52 minutes
• Self-Paced
• Free Video