Notions of Nonpositive Curvature and Groups - Lecture 1
Explorez les notions de courbure non positive et leur application à la théorie des groupes, en mettant l'accent sur les méthodes combinatoires et géométriques classiques.
Rank of 3-Manifold Groups - Lecture 3
Explore 3-manifold group ranks, covering Heegaard genus, Abert-Nikolov's work on rank growth, and geometric decompositions of hyperbolic 3-manifolds with bounded rank.
Rank of 3-Manifold Groups - Lecture 2
Explore 3-manifold group ranks, covering Heegaard genus, Abert-Nikolov's work on rank growth, and geometric decompositions of hyperbolic 3-manifolds with bounded rank.
Rank of 3-Manifold Groups - Part I
Explore 3-manifold group ranks, covering generation, Heegaard genus, growth in cover towers, mapping tori, and geometric decompositions of hyperbolic 3-manifolds.
3-Manifold Groups and the Cannon Conjecture - Part I
Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte. Examinez la conjecture de Cannon et ses variantes, ainsi que leurs connexions et critères.
Geometrization and its Consequences in 3-Manifold Topology - Part I
Explore Thurston's geometric perspective on 3-manifolds, including Perelman's Geometrization Theorem, and its implications for topology, algorithms, and group theory in 3-dimensional spaces.
Geometrization and Its Consequences in 3-Manifold Topology - Part II
Explore Thurston's geometric perspective on 3-manifolds, Perelman's Geometrization Theorem, and their impact on topology. Discover algorithmic and group-theoretic applications in 3-manifold theory.
Geometric Approaches to Artin Groups
Explore geometric approaches to Artin groups, focusing on constructing group actions on spaces with CAT(0), hyperbolic, or systolic geometries. Gain insights into recent progress and parabolic subgroups.
Outer Space for Right-Angled Artin Groups
Explore right-angled Artin groups and their automorphisms, bridging free and abelian groups. Discover a new "Outer Space" analogue for RAAGs and its potential applications in geometric group theory.
From Braid Groups to Artin Groups - Lecture 1
Explore Artin groups, including braid groups and free groups. Discover algebraic and geometric characterizations, current knowledge, and new approaches to challenging problems in this field.
Finite Index Rigidity of Hyperbolic Groups
Explore finite index rigidity of hyperbolic groups, examining tools and ideas for proving isomorphic finite index subgroups have the same index in non-elementary cases.
Strong Coherence of One-relator Groups
Explore strong coherence in one-relator groups, examining their geometric and algebraic properties in this advanced mathematical lecture.
Cubulating Drilled Bundles Over Graphs
Explore Gromov-hyperbolic surface bundles, drilling essential closed curves, and cubulability conditions in relatively hyperbolic fundamental groups with peripheral Z+Z groups.
Local Connectivity of the Boundary of a Relatively Hyperbolic Group
Explore local connectivity of boundaries in relatively hyperbolic groups, extending Gromov's results to a more general setting without restrictions. Gain insights into geometric group theory.
The Coherence of One-Relator Groups
Explore the coherence of one-relator groups, focusing on Baumslag's conjecture and its proof. Gain insights into finitely generated subgroups and their presentations in group theory.
The Markov Ordering of the Rationals
Explore hyperbolic geometry's role in characterizing monotonicity of rational number ordering on a modular torus, connecting to Diophantine approximation and number theory.
Subgroup Distortion in Hyperbolic Groups
Explore subgroup distortion in hyperbolic groups, surveying known functions and examining new examples constructed with Tim Riley.
Banded Projections to Z-factor Graph - Lecture
Explore baneled projections to Z-factor graphs in subgroup geometry, delving into advanced mathematical concepts and their applications.
Subgroups of Hyperbolic Groups, Finiteness Properties and Complex Hyperbolic Lattices
Explore finiteness properties of subgroups in hyperbolic groups and complex hyperbolic lattices, focusing on cocompact arithmetic lattices with positive first Betti number.
Outer Spaces of Virtually Free Groups - Lecture on Group Theory
Explore the deformation space of trees in virtually free groups, relating it to Outer Space of free subgroups. Understand equivalence and actions on trees with finite stabilizers.
Rational Curvature Invariants of 2-Dimensional Complexes
Explore new rational curvature invariants of 2-complexes, unifying theories of various families and their potential applications in geometric group theory.