On Distortion Elements, Orderability and Regularity in Groups
Explore distortion elements in groups, examining their properties and implications for orderability and regularity in finitely-generated orderable groups.
Small Cusped Hyperbolic 3-Manifolds and Order-Preserving Braids
Explore minimal-volume cusped hyperbolic 3-manifolds and their fundamental groups' orderability. Investigate order-preserving braids and their impact on Artin actions.
On Context-Free Orderings on Free Products
Explore context-free orderings on free products, including constructions of Cantor sets with dense subsets of context-free orders and extensions to free products with regularly ordered factors.
Generalized Torsion Elements as Generalizations of Torsion Elements
Explore generalized torsion elements in group theory, their impact on bi-orderability, and connections to the Alexander polynomial. Gain insights into advanced mathematical concepts.
R-Focal Actions of Groups Acting on the Line
Explore R-focal actions of groups on the real line, examining examples and applications to understand group action spaces in homeomorphisms.
Detecting 3-Manifold Groups Among Circularly Ordered Groups
Explore techniques for identifying 3-manifold groups within circularly ordered groups, focusing on mathematical detection methods and group theory applications.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond
Explore countable subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions. Examine model theory applications.
Spaces of Actions on the Line
Explore finitely generated group actions on the line, examining compact laminations and Deroin spaces through examples and collaborative research insights.
Introduction to Circular Orderings - Lecture 2
Explore algebraic and combinatorial aspects of circularly-orderable groups, focusing on cohomology, central extensions, and obstruction spectra. Gain insights through exercises and open problems.
Introduction to Circular Orderings - Lecture 3
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 1
Explore countable subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions. Gain insights into model theory applications.
Introduction to Order Structures in Groups - Lecture 4
Explore order structures in groups, covering total orders, algebraic structures, and essential tools. Gain insights into open problems and active research areas in the field.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 2
Explore finitely generated subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 3
Explore finitely generated subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions.
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.
Introduction to Order Structures in Groups - Lecture 2
Explore various total orders on groups, their relationships with algebraic structures, and essential tools like dynamical realization and the Burns-Hale theorem.
Introduction to Order Structures in Groups - Lecture 1
Explore various types of total orders on groups, their relationships with algebraic structures, and essential tools like dynamical realization and the Burns-Hale theorem.
Acylindricity of the Cremona Group - Part 2
Explore the Cremona group's action on infinite-dimensional hyperbolic space and its acylindrical hyperbolicity, leading to insights on its SQ-universal property and embeddings of countable groups.
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.