Detects right-veering properties in open books using combinatorial methods.
problem Determining the right-veering property of contact structures.
method Combinatorial approach to detect left-veering arcs in open books.
result Existence of an algorithm to detect right-veering for compact surfaces.
Study on finiteness property of right-angled Artin groups actions on extension graphs.
problem Finiteness property of hyperbolic simplicial actions on right-angled Artin groups.
method Analysis of right-angled Artin group actions on extension graphs, using asymptotic translation lengths and syllable lengths.
result Asymptotic translation lengths of elements in right-angled Artin groups are rational and have a common denominator under certain conditions.
In this article, we discuss the quasiconformal structure of boundaries of right-angled hyperbolic buildings using combinatorial tools. In particular we exhibit some examples of buildings of dimension 3 and 4 whose boundaries satisfy the combinatorial Loewner property. This property is a weak version of the Loewner prop…
New knot found with unique property.
problem Existence of hyperbolic fibered slice knots with specific monodromy.
method Constructed a specific type of hyperbolic fibered slice knot.
result Negative answer to a question posed by Hubbard et al.
We introduce the class of perturbed right-angled Artin groups. These are constructed by gluing Bieri double groups into standard right-angled Artin groups. As a first application of this construction we obtain families of CAT(0) groups containing finitely presented subgroups which are not of type FP3, and h…
The paper defines circular orderability for quandles and explores their properties.
problem Understanding the structure of quandles through circular orderings.
method Introduced circular orderability for quandles, showed embedding properties, and provided examples.
result Spaces of circular orderings embed in the space of all orderings, and examples of non-circularly orderable quandles are given.
Our work extends Coase's theorem to settings with uncertainty, showing how to maximize social welfare through property rights and learning.
problem Theoretical models of externality often assume perfect knowledge, limiting practical solutions.
method We extend Coase's theorem to a two-player bandit setting with uncertainty, designing a learning policy to maximize social welfare.
result We show that property rights and learning can recover Coase's theorem in settings with uncertainty.
Constructs a support-preserving homotopy for differential forms with boundary decay estimates.
problem Non-uniqueness of chain homotopies in de Rham complexes with boundary decay properties.
method Constructs a specific chain homotopy with desirable support propagation and boundary decay estimates.
result Obtains a support-preserving right inverse of the divergence operator with optimal decay estimates.
The paper proves geodesics and conic sections are length-minimizing under specific metrics.
problem Finding shortest paths in complex geometries.
method Calibrations and conformal metrics.
result Geodesics and conic sections are length-minimizing.
The study examines subgroups of RACGs and RAAGs, focusing on their RAAG properties.
problem Characterizing subgroups of right-angled Coxeter and Artin groups that are themselves RAAGs.
method Analyzes specific classes of subgroups and uses quasi-isometry and commensurability properties.
result Characterizes finite-index visual RAAG subgroups of 2-dimensional RACGs and provides new examples of RACGs commensurable to RAAGs.
A closed braid naturally gives rise to a transverse link in the standard contact 3-space. We study the effect of the dynamical properties of the braid monodromy, such as right-veering, on the contact-topological properties of the transverse link and its transverse invariants in knot Floer and Khovanov homologies. In pa…
Convex domains have a unique boundary property related to normal vectors.
problem Characterizing convex domains using boundary properties and inequalities.
method Proving an inequality involving boundary normal vectors and distances.
result A constant cn exists such that the inequality holds for convex domains, with equality if and only if the domain is convex. Homology growth of specific mapping tori vanishes for certain groups.
problem Homology growth of polynomially growing mapping tori in various groups.
method Proof of the cheap rebuilding property for specific groups.
result Torsion homology growth vanishes for Farber sequences in every degree.
Fair market valuations ignore future worker profits in employee-owned firms.
problem Ignoring future worker profits in fair market valuations for employee-owned firms.
method Analyzing property rights and residual claimants in employee-owned firms.
result Fair market valuations are inappropriate for employee-owned firms.
Associated to each material body B there exists a groupoid Ω(B) consisting of all the material isomorphisms connecting the points of B. The uniformity character of B is reflected in the properties of Ω(B): B is uniform if,…
In this paper we introduce the Constant Width Measure Set, which measures the constant width property of an oval, i.e. the planar simple closed strictly convex curve. We study its geometrical properties. We find the exact relation between the length and the area of the region bounded by an oval M. Namely, the followi…
New groups algebraically fibre with high-dimensional hyperbolic groups.
problem Finding new quasi-isometry classes of hyperbolic groups.
method Constructing infinitely many hyperbolic groups as finite-index subgroups of right-angled Coxeter groups.
result Groups algebraically fibre with finitely presented kernels, expanding finiteness properties.
The paper studies fibering properties of RACGs and random subcomplexes of buildings.
problem Higher virtual algebraic fibering properties of right-angled Coxeter groups.
method Generalization of Bestvina-Brady discrete Morse theory applied to Davis complex, combined with probabilistic arguments.
result Commutator subgroups of RACGs with certain finite building flag complexes admit epimorphisms to Z with strong topological finiteness properties.
Improved bounds on acylindricity for right-angled Artin groups.
problem Bounding the acylindrical action of right-angled Artin groups on their extension graphs.
method Exploring lattice properties, studying prefixes of powers, and extending quasi-root uniqueness.
result Cardinality of r-quasi-stabilizer is bounded by a linear function of r. We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e. they have full density with respect to counting in balls for the word metric) and translation length grows linearly. We provide applications t…
The paper proves properties of specific hypersurfaces in a 5-sphere.
problem Characterizing closed minimal hypersurfaces with constant curvature.
method Analyzing the curvature properties and using isoparametric functions.
result Closed minimal hypersurfaces in S5(1) have specific forms. Paper examines how adversarial ML attacks and defenses impact civil liberties and human rights.
problem Impact of adversarial machine learning on civil liberties and human rights.
method Uses insights from STS, anthropology, and human rights literature.
result Adversarial defenses can be used to suppress dissent and limit investigation of ML systems.
Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erdös-Rényi model). In this paper, we extend this model to study random general Coxeter groups and give some results about random Coxeter groups, including some information about t…
Groups with specific properties have similar cubulations and coarse median structures.
problem Understanding the structure of certain groups through cubical coarsening.
method Analyzing right-angled Artin and Coxeter groups, focusing on automorphisms and cubulations.
result Automorphisms of specific groups preserve coarse median structures and have nice fixed subgroups.
We investigate the rank gradient and growth of torsion in homology in residually finite groups. As a tool, we introduce a new complexity notion for generating sets, using measured groupoids and combinatorial cost. As an application we prove the vanishing of the above invariants for Farber sequences of subgroups of righ…
In many developing countries intellectual property infringement and the commerce of pirate goods is an entrepreneurial activity. Digital piracy is very often the only media for having access to music, cinema, books and software. At the same time, bio-prospecting and infringement of indigenous knowledge rights by intern…
We consider relative normalizations of ruled surfaces with non-vanishing Gaussian curvature K in the Euclidean space R3, which are characterized by the support functions (α)q=∣K∣α for α∈R (Manhart's relative normalizations). All ruled surfaces for…
Study character varieties of a Coxeter group in hyperbolic and Anti-de Sitter spaces.
problem Characterize the geometric transitions of a Coxeter group's holonomy representations.
method Analysis of rigidity properties and character varieties in hyperbolic and Anti-de Sitter spaces.
result Description of singularity at the collapse of a right-angled cuboctahedron.
Study on symmetric automorphisms of RAAGs, proving finiteness properties and contractibility.
problem Finiteness properties and contractibility of symmetric automorphisms of RAAGs.
method Definition of symmetric automorphism group, construction of symmetric Outer space, proof of contractibility.
result Finiteness properties and contractibility results for symmetric automorphisms of RAAGs.
Extends growth properties of hyperbolic groups to their extensions.
problem Quantifying subgroup alternatives in group laws.
method Develops a framework for preserving exponential growth in extensions of hyperbolic groups.
result Automorphism groups of certain hyperbolic and Artin groups have locally uniform exponential growth.
The paper connects sectional category and parametrized Borsuk-Ulam property for fibrations.
problem Parametrized Borsuk-Ulam property for fibrations.
method Investigation of sectional category connections and fibrations.
result The sectional category of q being larger than qp′ implies the parametrized Borsuk-Ulam property for the triple (p,τ;p′). The paper studies right-angled links on higher genus surfaces.
problem Classifying and understanding right-angled links on surfaces of higher genus.
method Defining and proving equivalence of properties for RGCR links, using diagram restrictions and polygonal checkerboard surfaces.
result Classification of RGCR links and bounds on their number for a given genus.
We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group A(K) has such a subgroup if its defining graph K contains an n-hole (i.e. an induced cycle of length n) with n≥5. We construct another eight "forbidden" grap…
The paper discusses triangulations of Gromov sets and their properties.
problem Understanding triangulations of Gromov subsets in metric spaces.
method Review and extension of Chew's triangulation result for η-Gromov subsets of R2, and construction of subdivisions with controlled edge lengths and angles. result The existence of geodesic triangulations with controlled side lengths and angles for compact Riemannian 2-manifolds.
Study on visibility properties of spiral sets in higher dimensions.
problem Characterizing density properties of spiral sets.
method Employing visibility concepts from discrete geometry.
result Established conditions for various density properties of spirals.
Study the module structure of homology of Artin kernels.
problem Characterize the module structure of homology of Artin kernels.
method Use flag complex and double covers of toric complexes to analyze properties of torsion part.
result Determine dimensions and sizes of Jordan forms of the torsion part.
New bound for group action length without diameter restriction.
problem Bounding minimal translation length for Artin groups.
method Graph theoretic properties of biconnected graphs.
result Upper bound of 2 for minimal translation length holds without diameter restriction.
Study presentations of groups that can be generalised over continuous open group monomorphisms.
problem Investigate presentations of groups that can be generalised over continuous open group monomorphisms.
method Systematic study of presentations with generalisation properties, focusing on right-angled Artin groups (RAAGs).
result Establish high connectivity properties for universal Salvetti-type complexes and novel examples of LC groups with prescribed compactness properties.
For a finite simplicial graph Γ, let G(Γ) denote the right-angled Artin group on the complement graph of Γ. In this article, we introduce the notions of "induced path lifting property" and "semi-induced path lifting property" for immersions between graphs, and obtain graph theoretical criteria for the embedabilit…
Study non-degeneracy of minimal hypersurfaces asymptotic to cones, proving Jacobi equation solvability.
problem Non-degeneracy properties of minimal hypersurfaces asymptotic to cones.
method Analysis of the Jacobi operator and construction of its right inverse.
result Proved solvability of the Jacobi equation under non-degeneracy assumptions.
Over the past decades, numerous loss functions have been been proposed for a variety of supervised learning tasks, including regression, classification, ranking, and more generally structured prediction. Understanding the core principles and theoretical properties underpinning these losses is key to choose the right lo…
Let ψ be a multi-dimensional random variable. We show that the set of probability measures Q such that the Q-martingale StQ=EQ[ψ∣Ft] has the Martingale Representation Property (MRP) is either empty or dense in L∞-…
Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified framework for studying the mapping class group, right-angled Artin and Coxeter groups, and many 3--manifold groups. We investigate strongly quasiconvex subsets in this class and characterize them in terms of their contracting pro…
Develops a method for solving optimal stopping problems with multiple exercise rights.
problem Optimal stopping with multiple exercise rights under model uncertainty.
method Pathwise duality approach based on robust martingale dual representation.
result Establishes upper and lower bounds that converge to the true solution.
A Deep Zero-Inflated Model for Detecting North Atlantic Right Whale Presence
problem Balancing marine conservation and blue economy management
method Deep Zero-Inflated Bernoulli model
result Improved model adequacy and predictive performance
This research introduces Lie brackets on spaces of biderivations in Lie algebras.
problem Understanding higher-order infinitesimal symmetries in Lie algebras.
method Study of right biderivations and Lie brackets on their spaces.
result New Lie algebra framework for biderivations with applications in deformation theory.
Groups of importance in group theory have flexible stability properties.
problem Stability and flexibility of groups in geometric and combinatorial group theory.
method Establishing Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for specific groups.
result Groups like 3-manifold groups, limit groups, and certain one-relator groups are very flexibly stable. We investigate the combinatorial and geometric properties of automorphism groups of universal right-angled Coxeter groups, which are the automorphism groups of free products of copies of Z_2. It is currently an open question as to whether or not these automorphism groups have non-positive curvature. Analogous to Outer …