Lower bound on colors needed for non-zero determinant links.
problem Finding the minimum number of colors for non-zero determinant links.
method Proved a lower bound using logarithmic function.
result Minimal number of colors is at least 1 + log2(n).
Study of singularities in two-dimensional Nijenhuis operators with non-zero trace differential.
problem Characterizing singularities of two-dimensional Nijenhuis operators.
method Analyzing the smoothness of functions related to the determinant of the operator.
result Complete description of singularities for certain function classes.
The paper bounds the first eigenvalue of toric Kähler manifolds and identifies specific metrics.
problem Bounding the smallest non-zero eigenvalue of the Laplacian on toric Kähler manifolds.
method Explicit upper bound for the eigenvalue in terms of moment polytope data; equivariant counterpart analysis.
result Explicit upper bound for the eigenvalue and identification of metrics achieving this bound.
Ozsváth-Szabó proved the property that any coefficient of Alexander polynomial of lens space knot is either ±1 or 0 and the non-zero coefficients are alternating. Combining the formulas of the Alexander polynomial of lens space knots due to Kadokami-Yamada and Ichihara-Saito-Teragaito, we refine Ozsváth-Szabó's p…
In this paper we use character variety methods to study homomorphisms between the fundamental groups of 3-manifolds, in particular those induced by non-zero degree maps. A {\it knot manifold} is a compact, connected, irreducible, orientable 3-manifold whose boundary is an incompressible torus. A {\it virtual epimorphis…
The study explores Legendrian invariants and half Giroux torsion in contact structures.
problem Understanding Legendrian invariants and their behavior with half Giroux torsion.
method Analysis of Legendrian links with non-vanishing contact invariants and the study of half Giroux torsion.
result Null-homologous links with irreducible complements have non-loose Legendrian realizations with non-zero invariants.
The n-dimensional torus is uniquely characterized by specific harmonic forms.
problem Characterizing the n-dimensional torus via harmonic forms.
method Analyzing closed 1-forms on the torus to determine unique properties.
result The n-dimensional torus is the unique manifold supporting a linearly independent set of (n-1) closed 1-forms whose product determines a non-zero cohomological class.
Conformally compact and complete smooth solutions to the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton using the first Pontrjagin form of the (-)-connection} on 6-dimensional non-Kaehler nilmanifold are presented. In the conformally compact case the dilaton is determined by t…
We give some applications of the Chern Simons gauge theory to the study of the set vol(N,G) of volumes of all representations $ρ\coπ_1N\to G$, where N is a closed oriented three-manifold and G is either ${\rm Iso}_e\t{\rm SL_2(\R)}$, the isometry group of the Seifert geometry, or ${\rm Iso}_+{\Hi}^3$, the o…
Investigates portfolio selection for rank-dependent utilities in incomplete markets.
problem Portfolio selection for agents with rank-dependent utility in incomplete financial markets.
method Characterizes deterministic strict equilibrium strategies for constant-coefficient and time-invariant probability weighting functions. Addresses the issue of selecting an optimal strategy from multiple equilibrium strategies for time-variant probability weighting functions.
result Characterizes deterministic strict equilibrium strategies and identifies optimal strategies from multiple equilibrium strategies.
Rodent identifies ODEs from trajectories without needing basis functions.
problem Identifying the generating ODE from observed system trajectories.
method Uses Neural Arithmetic Units and sparsification techniques (VAE and ARD) to minimize state size and non-zero parameters.
result Learned models represent a manifold of ODEs including harmonic signals and Lotka-Volterra systems.
Study on left orderability of specific knot covers.
problem Determining left orderability of knot covers.
method Computing nonabelian SL2(C) character varieties and analyzing real points.
result Left orderability of fundamental groups of cyclic branched covers.
We study the class of spacelike surfaces in the four-dimensional Minkowski space whose mean curvature vector at any point is a non-zero spacelike vector or timelike vector. These surfaces are determined up to a motion by eight invariant functions satisfying some natural conditions. The subclass of Chen surfaces is char…
New symmetries found in Riemann-Cartan geometries.
problem Investigating symmetries in geometries with curvature and torsion.
method Mathematical tools to determine symmetries and subclasses of geometries.
result Determined all static and stationary spherically symmetric Riemann-Cartan geometries and subclasses with specific symmetries.
Study Nash equilibrium in non-zero-sum game with Bermudan strategies.
problem Optimizing pay-offs in non-linear non-zero-sum games.
method Recursive construction to find Nash equilibrium.
result Existence of Nash equilibrium in non-zero-sum game.
Study finds new factorable surfaces with non-zero curvature in pseudo-Galilean space.
problem Classifying surfaces with non-zero curvature in pseudo-Galilean space.
method Analyzing factorable surfaces as graphs of product functions.
result New classification results for factorable surfaces with non-zero Gaussian and mean curvature.
In this paper we develop a new technique that yields infinitely many surface bundles with non-zero signature.
4-manifolds with non-hyperbolic geometry are ordered.
problem Ordering 4-manifolds with non-hyperbolic Thurston geometry.
method Derived from closed aspherical 4-manifolds and maps of non-zero degree.
result Kodaira dimension is monotone with maps of non-zero degree.
Study self-interaction effects on point particle construction in GR.
problem Understanding mass in point particle initial data in GR.
method Introduce framework, rigorously prove vanishing mass, identify geometric structure and scaling parameter.
result Identify conditions for non-zero mass in point particle construction.
Simplifies NL models by approximating them as LPV systems and identifying NL subterms.
problem Complex NL models are hard to interpret and impractical.
method Linear approximation around operating points, sparse estimation in RKHS, LPV model reduction.
result Identifies NL subterms and their input spaces in sparse additive NL models.
The study characterizes biharmonic surfaces in specific 3-manifolds.
problem Characterizing biharmonic surfaces in non-Sasakian contact metric 3-manifolds.
method Characterization through scalar curvature and mean curvature.
result Examples of biharmonic submanifolds constructed and determined 3-manifolds with proper biharmonic foliations.
We show that a bi-invariant metric on a compact connected Lie group G is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric g0 on G there is a positive integer N such that, within a neighborhood of g0 in the class of left-invariant metrics of a…
We complete the reduction of Sasakian manifolds with the non-zero case by showing that Willett's contact reduced space is compatible with the Sasakian structure. We then prove the compatibility of the non-zero Sasakian (in particular, contact) reduction with the reduction of the Kähler (in particular, symplectic) cone.…
New groups prevent maps from direct products on certain aspherical manifolds.
problem Preventing maps of non-zero degree from direct products on aspherical manifolds.
method Defining new groups and proving properties of aspherical manifolds.
result Certain aspherical manifolds do not admit maps of non-zero degree from direct products.
In a recent paper we defined a new filtration of the mapping class group--the "Lagrangian" filtration. We here determine the successive quotients of this filtration, up to finite index. As an application we show that, for any additive invariant of finite-type (e.g. the Casson invariant), and any level of the Lagrangian…
Sharp bounds found for the first non-zero Steklov eigenvalue.
problem Finding bounds for the first non-zero Steklov eigenvalue.
method Analyzing star-shaped domains and balls with smooth boundaries.
result Sharp lower and two-sided bounds for the first non-zero Steklov eigenvalue.
No regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces are found.
problem Existence of regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces.
method Analyzing polynomials defining hypersurfaces of various degrees and shapes.
result Hyperspheres and round cylinders are the only such hypersurfaces defined by polynomials of degree ≤3.
The study constructs geometrically decomposable aspherical 4-manifolds with non-zero signature and explores their properties.
problem Characterizing geometrically decomposable aspherical 4-manifolds with non-zero signature.
method Constructing examples and proving inequalities for geometrically decomposable aspherical 4-manifolds.
result All geometrically decomposable aspherical 4-manifolds with non-zero signature satisfy the inequality \( \chi \geq 3|σ| \).
This paper gives a polynomial invariant for flat virtual links. In the case of one component, the polynomial specializes to Turaev's virtual string polynomial. We show that Turaev's polynomial has the property that it is non-zero precisely when there is no filamentation of the knot, as described by Hrencecin and Kauffm…
Study finite group actions on manifolds with non-zero degree maps to nilmanifolds.
problem Understanding finite group actions on manifolds with specific properties.
method Analyzes effective actions, bounds discrete degrees, studies toral rank conjecture, and introduces iterated actions.
result Proves Homeo(M) is Jordan and bounds the discrete degree of symmetry.
A little complement concerning the dynamics of non-metric manifolds is provided, by showing that any flow on an ω-bounded surface with non-zero Euler character has a fixed point.
Study ruled surfaces with non-zero Gaussian curvature in Euclidean space.
problem Characterize ruled surfaces with non-zero Gaussian curvature.
method Use relative normalizations and analyze properties of surfaces like Pick invariant and Tchebychev vector field.
result Determine specific properties of ruled surfaces with non-zero Gaussian curvature.
Kerr spacetimes without closed null geodesics for non-zero rotation.
problem Analyzing closed geodesics in Kerr spacetimes.
method Analytic extension and geodesic analysis.
result Kerr spacetimes do not admit closed null geodesics for any non-zero rotation parameter.
Symplectic structures on graded manifolds are explored.
problem Exploring symplectic structures on graded manifolds.
method Definition and analysis of symplectic Z2n-manifolds. result Generalization of symplectic geometry to higher graded settings.
The rational homotopy type of certain manifolds is determined by their cohomology and Bianchi-Massey tensor.
problem Determining the rational homotopy type of (n-1)-connected manifolds.
method Defining the Bianchi-Massey tensor and using it to prove the rational homotopy type is determined by cohomology and tensor.
result The rational homotopy type of (n-1)-connected manifolds of dimension up to 5n-3 is determined by their cohomology and Bianchi-Massey tensor.
Recently, we developed a method for the study of holonomy properties of non-Riemannian Finsler manifolds and obtained that the holonomy group can not be a compact Lie group, if the Finsler manifold of dimension >2 has non-zero constant flag curvature. The purpose of this paper is to move further, exploring the holon…
The paper quantizes vortex moduli spaces on compact Kahler surfaces using determinant bundles.
problem Quantizing vortex moduli spaces on compact Kahler surfaces.
method Developed holomorphic determinant bundles and geometric quantization for vortex moduli spaces.
result Quantized vortex moduli spaces on compact Kahler surfaces using determinant bundles.
The paper proves an inequality for the second non-zero eigenvalue of the Laplacian on the projective plane.
problem An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane.
method Analytical proof and geometric construction of limiting metrics.
result The second non-zero eigenvalue is not greater than 20π for metrics of unit area, with a specific limiting configuration.
The holonomy group G of a pseudo-quaternionic-Kählerian manifold of signature (4r,4s) with non-zero scalar curvature is contained in $\Sp(1)\cdot\Sp(r,s)$ and it contains $\Sp(1)$. It is proved that either G is irreducible, or s=r and G preserves an isotropic subspace of dimension 4r, in the last case, ther…
Estimates the first non-zero eigenvalue using Ricci curvature on graph edges.
problem Estimating the first non-zero eigenvalue of the Laplacian on graph edges.
method Defining edge distance, studying coarse Ricci curvature, and using Jost-Horak's Laplacian definition.
result Obtained an estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature for a regular graph.
Statistical Lie algebras with constant curvature are linked to locally conformally Kähler structures.
problem Characterizing Lie algebras with constant curvature and their geometric implications.
method Constructing statistical manifolds and Sasakian structures to relate Lie algebras to locally conformally Kähler structures.
result Statistical Lie algebras of constant curvature correspond to locally conformally Kähler Lie algebras.
Exact formulas for volumes of specific knot cone-manifolds.
problem Finding exact volumes of cone-manifolds with two-bridge knots.
method Provided exact integral formulas using Chebyshev polynomials and algebraic equations.
result Exact formulas for hyperbolic and spherical volumes of cone-manifolds.
Study shows non-abelian free groups' 4th cohomology is non-zero.
problem Proving non-vanishing of fourth bounded cohomology of free groups.
method Splitting argument applied to n-manifolds with codimension 2 submanifolds. result Non-zero fourth bounded cohomology of non-abelian free groups.
Sphere theorems for p-Laplacian eigenvalues established.
problem Sphere theorems for p-Laplacian eigenvalues.
method Established sphere theorems for p-Laplacian eigenvalues.
result Sphere theorems for p-Laplacian eigenvalues established.
First the title could be also understood as ``3-manifolds related by non-zero degree maps" or "Degrees of maps between 3-manifolds" for some aspects in this survey talk. The topology of surfaces was completely understood at the end of 19th century, but maps between surfaces kept to be an active topic in the 20th centur…
We construct new explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic equations of motion in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations…
We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasipositive and fibered ones, and show that 3-braid links have a unique incompressible Seifert surface. We also classify the positive braid wo…
We consider the problem of selecting non-zero entries of a matrix A in order to produce a sparse sketch of it, B, that minimizes ∥A−B∥2. For large m×n matrices, such that n≫m (for example, representing n observations over m attributes) we give sampling distributions that exhibit four importa…