A Journey from Statistical Mechanics to Number Theory
Explore connections between statistical mechanics and number theory, focusing on the Riemann zeta function and its relation to phase transitions in disordered systems.
Reducible but Indecomposable Representations in Mathematical Physics
Explore representation theory in non-unitary physical systems, focusing on reducible but indecomposable representations and their importance in statistical loop models and CFT.
K-tilings of the Aztec Diamond
Explore K-tilings of the Aztec diamond, a fascinating mathematical concept in integrable systems and exactly solvable models.
Crystal Bases in Statistical Mechanics, Representation Theory and Combinatorics - Part II
Explore crystal base theory applications in symmetric functions and cyclic sieving through combinatorial crystal definitions in statistical mechanics and representation theory.
Crystal Bases in Statistical Mechanics, Representation Theory and Combinatorics - Part I
Explore crystal base theory applications in symmetric functions and cyclic sieving through combinatorial definitions, enhancing understanding of statistical mechanics and representation theory.
Cluster Algebras and Hyperbolic Geometry
Explore the application of cluster algebra to 2D and 3D hyperbolic geometry, examining ideal triangulations, Teichmuller spaces, and knot volumes through mutations and cluster variables.
The Origin of Trigonometric K-matrices - Part I
Explore the mathematical foundations of quantum integrability with boundaries, focusing on K-matrices and their universal properties in relation to quantum affine algebras and reflection equations.
Integrability of Box-Ball Systems and Randomized Box-Ball Systems - Part II
Explore integrability and randomization in box-ball systems. Delve into crystals, Bethe ansatz, ultradiscretization, and analytical results from TBA and GHD. Gain insights into density plateaux and current correlations.
Finite Point Configurations in Euclidean, Discrete, and Arithmetic Settings
Explore finite point configurations across Euclidean, discrete, and arithmetic spaces. Discover size requirements for subsets containing congruent copies of given configurations, with connections to learning theory.
Orderability of 3-Manifold Groups and the L-Space Conjecture
Explore orderability of 3-manifold groups, focusing on the L-space conjecture and its connections to group orderability, taut foliations, and Heegaard Floer homology in hyperbolic 3-manifolds.
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.
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.