Introduction to Circular Orderings - Lecture 1
Explore algebraic and combinatorial aspects of circularly-orderable groups, covering definitions, group operations, cohomology, and obstruction spectra. Gain insights through exercises and open problems.
Introduction to Circular Orderings - Lecture 4
Explore algebraic and combinatorial aspects of circularly-orderable groups, focusing on cohomology, left-ordered central extensions, and obstruction spectra. Gain insights through exercises and open problems.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 4
Explore finitely generated subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions.
Fine Curve Graphs and Fragmentation - Lecture 3
Explore fine curve graphs and their applications in geometric group theory, focusing on fragmentation norms in surface homeomorphism groups and large-scale geometry.
The Structure of Homeomorphism Groups - Part I
Explore the rich algebraic structure of homeomorphism groups, their relation to manifold topology, and dynamics of group actions on manifolds.
Automorphisms of Groups and Higher Rank JSJ Decomposition
Explore automorphisms of hierarchically hyperbolic groups and a generalized JSJ decomposition, encoding algebraic structure and dynamics of automorphisms in higher rank settings.
Finite Quotients of Fibered, Cusped 3-Manifold Groups
Explore finite quotients of 3-manifold groups, leveraging mapping class group properties to study profinite completions of fibered hyperbolic 3-manifold fundamental groups.
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.
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.
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.
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.
Endperiodic Maps via Pseudo-Anosov Flows
Explore atoroidal, endperiodic maps on infinite-type surfaces through pseudo-Anosov flows, examining stretch factors, foliation cones, and entropy functions in topological dynamics.