Hyperbolic Groups Courses and Certifications

International Centre for Theoretical Sciences

Hyperbolic Geometry, Fuchsian Groups and Moduli Spaces - Lecture 1

Introducción a la geometría hiperbólica: modelos, propiedades y trigonometría. Exploración de los modelos del semiplano superior, disco y hiperboloide, con énfasis en geodésicas, ángulos y curvatura constante.

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

Centre International de Rencontres Mathématiques

Mapping Class Groups of Infinite-Type Surfaces and Their Actions on Hyperbolic Graphs

Explore mapping class groups of infinite-type surfaces and their actions on hyperbolic graphs in this advanced mathematical lecture by Priyam Patel.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups

Delve into advanced hyperbolic geometry concepts through an exploration of manifolds, submanifolds, and fundamental groups, with insights from leading mathematician Monika Kudlinska.

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

International Centre for Theoretical Sciences

Random Walks on Hyperbolic Groups by Peter Haissinsky

Explore random walks on hyperbolic groups in this lecture by Peter Haissinsky, covering fundamental concepts, techniques, and applications in geometric group theory and probability.

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

Centre de recherches mathématiques - CRM

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
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

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
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Hyperbolically Embedded Subgroups of Acylindrically Hyperbolic Groups - Lecture 2

Explore hyperbolically embedded subgroups in acylindrically hyperbolic groups, examining geometric properties, connections to random walks, and applications in proving key results.

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

Centre de recherches mathématiques - CRM

Hyperbolically Embedded Subgroups of Acylindrically Hyperbolic Groups - Lecture 3

Explore hyperbolically embedded subgroups in acylindrically hyperbolic groups, examining geometric properties, connections to random walks, and applications in proving key results.

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

Centre de recherches mathématiques - CRM

Hyperbolically Embedded Subgroups of Acylindrically Hyperbolic Groups - Lecture 1

Explore acylindrically hyperbolic groups through hyperbolically embedded subgroups. Investigate geometric properties, connections with random walks, and applications to important results in group theory.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Counting Limit Theorems for Representations of Gromov-Hyperbolic Groups

Explore limit theorems for Gromov-hyperbolic group representations, examining statistical results analogous to random matrix products theory for spherical averages in the S-metric.

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

Stony Brook Mathematics

A Finiteness Theorem for Gromov-Hyperbolic Groups

Explore a finiteness theorem for Gromov-hyperbolic groups, delving into δ-hyperbolic, torsion-free, non-cyclic marked groups with bounded entropy. Gain insights into the proof and key concepts.

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

Big Ideas In Dynamics

Random Walks on Weakly Hyperbolic Groups

Explore random walks on weakly hyperbolic groups, delving into advanced mathematical concepts and their applications in dynamics and group theory.

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

Institute for Advanced Study

Partially Hyperbolic Actions of Semisimple Lie Groups

Explore recent progress in classifying higher-rank semisimple group actions with uniformly expanding and contracting directions, building on Zimmer's foundational rigidity results.

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

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups

Delve into advanced hyperbolic geometry concepts with Jessica Purcell, exploring drilling and filling techniques for tame hyperbolic 3-manifolds and their fundamental properties in this mathematical lecture.

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

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups

Delve into advanced hyperbolic geometry concepts through an exploration of renormalized volume and isoperimetric profiles in hyperbolic manifolds, presented by Yale University's Franco Vargas.

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