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.
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.
Left-Orderability and Toroidal 3-Manifolds
Explore left-orderability in 3-manifolds with incompressible tori, using order-detection of slopes. Gain insights into the L-space conjecture through new evidence.
Non-standard Orders on Torus Bundles with One Boundary
Explore non-standard bi-orderings of fundamental groups in torus bundles with one boundary, extending Perron-Rolfsen's work on standard orderings and Alexander polynomials.
Off-Diagonal Spectral Cluster Asymptotics on Zoll Manifolds
Explore off-diagonal spectral cluster asymptotics on Zoll manifolds, examining universal asymptotic behavior of spectral cluster kernels and implications for monochromatic random waves in Riemannian geometry.
Riesz Inequality for Polygons: Symmetry and Symmetry Breaking
Explore counterparts of Hardy-Littlewood and Riesz inequalities for polygons, examining symmetry and symmetry breaking in nonlocal isoperimetric problems.
Eigenvalues and Minimal Surfaces
Explore Laplace operator eigenvalues, their physical significance, and connection to minimal surfaces. Discover recent findings in isoperimetric eigenvalue problems for Riemannian surfaces.
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.
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.
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.