Compute group cohomology for mapping class group with non-symplectic coefficients.
problem Compute group cohomology for mapping class group with non-symplectic coefficients.
method Compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group.
result First group cohomology computation for the mapping class group with non-symplectic coefficients.
We present some methods to construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or non-symplectic cyclic isotropy point sets. All such actions are not compatible with any symplectic form.
We show that K3 surfaces with non-symplectic automorphisms of prime order can be used to construct new compact irreducible G2-manifolds. This technique was carried out in detail by Kovalev and Lee for non-symplectic involutions. We use Chen-Ruan orbifold cohomology to determine the Hodge diamonds of certain complex thr…
New geometric examples of involutions on Hilbert square K3 surfaces.
problem Existence of non-symplectic involutions on Hilbert square K3 surfaces.
method Geometric constructions of involutions on IHS manifolds.
result New examples of involutions proven to exist.
We show that sufficiently irreducible totally non-symplectic Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.
We study K3 surfaces with a pair of commuting involutions that are non-symplectic with respect to two anti-commuting complex structures that are determined by a hyper-Kähler metric. One motivation for this paper is the role of such Z22-actions for the construction of G2-manifolds. We find a large class …
Let S be a K3 surface that admits a non-symplectic automorphism ρ of order 3. We divide S×P1 by ρ×ψ where ψ is an automorphism of order 3 of P1. There exists a threefold ramified cover of a partial crepant resolution of the quotient that is a Calabi-Yau orbifold. We compute the …
Constructs projective moduli spaces for Calabi-Yau pairs.
problem Creating projective moduli spaces for Calabi-Yau surface pairs.
method Constructs projective asymptotically good moduli spaces.
result Provides a wall crossing between KSBA and K-moduli spaces.
We show that a large class of non-metric, non-symplectic affine holonomies can be realized, uniformly and without case by case considerations, by Weyl connections associated to the natural AHS-structures on certain generalized flag manifolds.
We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors, the latter `matching' via a certain non-holomorphic map. Suitable examples of threefolds …
Let M be $\CP#2\CPb$, $3\CP#4\CPb$ or $(2n-1)\CP#2n\CPb$ for any integer n≥3. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structure…
The paper proves symplectic neighbourhood theorems for stratified subspaces.
problem Finding symplectic neighbourhoods of stratified subspaces.
method Analogy with Weinstein's neighbourhood theorem, strong version of Moser's trick, and tubular neighbourhood theorem.
result Generalization of existing constructions for exotic Lagrangians.
Study classifies Calabi-Yau threefolds with non-Gorenstein involutions.
problem Understanding non-Gorenstein involutions on Calabi-Yau threefolds.
method Classification of Calabi-Yau threefolds with specific properties.
result Classification of Calabi-Yau threefolds with Picard rank one and non-Gorenstein involutions.
We describe a class of compact G2 orbifolds constructed from non-symplectic involutions of K3 surfaces. Within this class, we identify a model for which there are infinitely many associative submanifolds contributing to the effective superpotential of M-theory compactifications. Under a chain of dualities, these can…
Study semi-Kähler structures on specific Lie groups without symplectic structures.
problem Exploring structures on Lie groups without symplectic structures.
method Defined semi-Kähler and almost para-semi-Kähler structures on specific Lie groups.
result Geometric properties of these structures are studied.
The usual formulation of time-dependent mechanics implies a given splitting Y=R×M of an event space Y. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The goal is the frame-covariant formulation of time-dependent mechanics on a bundle…
The paper compares numerical schemes for nonholonomic systems using retraction maps.
problem Optimal control of nonholonomic systems with numerical approximations.
method Retraction maps used as seed for geometric integrators of Hamilton equations.
result Performance comparison of symplectic and non-symplectic integrators.
This is the sequel to the author's previous paper which gives an extension of Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds. The main result of this paper asserts the following. Whenever the Seiberg-Witten invariants are defined over a closed minimal 4-manifold X, they are equivalent modulo 2 to "near-symplecti…
The paper constructs Ricci-flat Kähler manifolds with specific decay properties.
problem Finding Ricci-flat Kähler manifolds with controlled decay rates.
method Geometric existence proof and construction of ansatz.
result Existence of 39 distinct Ricci-flat Kähler 3-folds with specific asymptotic angles.
Motivated by the construction of H. Endo and Y. Gurtas, changing a positive relator in Dehn twist generators of the mapping class group by using lantern substitutions, we show that 4-manifold $K3#2\CPb$ equipped with the genus two Lefschetz fibration can be rationally blown down along six disjoint copies of the configu…
New symplectic 4-manifolds with non-negative signatures are constructed using complex surfaces and quotients.
problem Creating new symplectic 4-manifolds with non-negative signatures.
method Using complex surfaces, Cartwright-Steger surfaces, and Hirzebruch's line-arrangement surfaces, along with quotients.
result Irreducible symplectic and non-symplectic 4-manifolds homeomorphic but not diffeomorphic to (2n−1)CP2#(2n−1)CPˉ2 are constructed. Study Lefschetz fibrations with 4D fibers using Seiberg-Witten theory.
problem Constraints on the topology of Lefschetz fibrations with 4D fibers.
method Using the family Bauer-Furuta invariant and framed bordism class of 1D Seiberg-Witten moduli spaces.
result New obstructions to the smooth isotopy of compositions of Dehn twists.
We construct new families of non-hyperelliptic Lefschetz fibrations by applying the daisy substitutions to the families of words (c1c2⋯c2g−1c2gc2g+12c2gc2g−1⋯c2c1)2=1, (c1c2⋯c2gc2g+1)2g+2=1, and (c1c2⋯c2g−1c2g)2(2g+1)=1 in the mapping …
In \cite{AP3, AHP}, the first author and his collaborators constructed the irreducible symplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n−1)CP2#(2n−1)CP2 for each integer n≥25, and the families of simply connected irreducible nonspin symplectic 4…
For a closed oriented smooth 4-manifold X with b+2(X)>0, the Seiberg-Witten invariants are well-defined. Taubes' "SW=Gr" theorem asserts that if X carries a symplectic form then these invariants are equal to well-defined counts of pseudoholomorphic curves, Taubes' Gromov invariants. In the absence of a symplectic f…
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured b…
Formula connects linking coefficients to Kontsevich integral coefficients.
problem Linking coefficients from Kontsevich integral.
method Purely combinatorial approach.
result Expresses linking coefficients as combinations of Kontsevich integral coefficients.
Computed distortion coefficients for the α-Grushin plane.
problem Analyzing the distortion coefficients of the α-Grushin plane.
method Using generalised trigonometric functions and synthetic curvature conditions.
result Estimates for distortion coefficients and a curvature condition conjecture.
Machine learning predicts Kronecker coefficients with high accuracy.
problem Predicting Kronecker coefficients from tensor products of symmetric group representations.
method Training machine learning models (NN, CNN, GBDT) to classify Kronecker coefficients as zero or non-zero.
result Trained models achieve high accuracy (≈0.98) in classifying Kronecker coefficients. Abstract: Determines thermoelastic coefficients from boundary data.
problem Determining coefficients of thermoelastic system from boundary information.
method Explicit expression for thermoelastic Dirichlet-to-Neumann map with variable coefficients.
result Thermoelastic Dirichlet-to-Neumann map uniquely determines coefficients on the manifold.
New filling functions for groups with coefficients show different asymptotic behavior.
problem Difficulty in filling loops with surfaces in Cayley graphs.
method Defining homological filling functions with coefficients and proving their differences.
result Filling functions for n-cycles with coefficients in different groups have distinct asymptotic behavior. Abstract: Determines Lamé coefficients from boundary measurements.
problem Determining Lamé coefficients from elastic boundary measurements.
method Explicit symbol of elastic Dirichlet-to-Neumann map, partial derivatives determination.
result Elastic Dirichlet-to-Neumann map uniquely determines Lamé coefficients.
Defines and proves properties of weighted renormalized volume coefficients.
problem None explicitly stated; focuses on mathematical definitions and proofs.
method Defines weighted renormalized volume coefficients and proves their variational nature and polynomial representation.
result Weighted renormalized volume coefficients are variational and can be expressed as polynomials of specific tensors.
Improved 3D LiDAR data classification using product coefficients.
problem Enhancing accuracy in 3D LiDAR data classification.
method Introducing product coefficients derived from measure theory as additional features in the classification process, alongside PCA.
result Significant improvement in classification accuracy with product coefficients.
High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current understanding of galaxy formation and evolution rests sensitively on relationships between…
We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced) Tait graph of the link projection. This leads us to introduce a free polynomial algebra of invariants of graphs whose ele…
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
problem Understanding Kaehler-Einstein metrics and their epsilon functions.
method Computes the third coefficient in the TYCZ-expansion of the epsilon function.
result Discovers the vanishing of the third coefficient's significance.
Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.
problem Local elliptic regularity for operators with low regularity coefficients in Sobolev-type spaces.
method Rescaling estimates and multiplication results for function spaces.
result Unified set of interior estimates and regularity inference for operators with Sobolev-type coefficients.
The paper uses Floer homology to study twist coefficients and their behavior after capping off.
problem Behavior of twist coefficients after capping off a boundary component.
method Heegaard Floer homology to constrain twist coefficients.
result Results about fractional Dehn twists and Floer homology of cyclic branched covers.
Extends A-type coefficient polynomials to B-type setting, introducing new invariants.
problem Tackles the B-type skein relation and introduces new coefficient polynomials.
method Introduces coefficient polynomials associated with the B-type skein relation and proves their invariance under Reidemeister moves.
result Shows that the generating series of these coefficient polynomials recovers the Kauffman polynomial.
We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
Bounding twist number of surface links using polynomial coefficients.
problem Bounding the twist number of alternating surface links.
method Introducing a generalized homological Kauffman bracket and applying it to surface link diagrams.
result A bound for the twist number of alternating surface links in terms of polynomial coefficients.
Characterizes differential forms and vector fields with constant coefficients on manifolds.
problem Understanding constant coefficient differential forms and vector fields on manifolds.
method Analyzes differential forms and vector fields of specific degrees, proving obstructions and characterizing solutions to partial differential systems.
result Characterizes differential forms and vector fields with constant coefficients of various degrees on smooth manifolds.
Study on gradient descent in Hilbert spaces with Markov chains, focusing on mixing coefficients.
problem Analyzing convergence of gradient descent in Hilbert spaces with stationary Markov chains.
method Examined strictly stationary Markov chains with φ- and β-mixing coefficients, derived probabilistic upper bounds. result Probabilistic upper bounds on convergence behavior of gradient descent algorithm based on mixing coefficients.
In this paper we use wavelet concepts to show that correlation coefficient between two financial data's is not constant but varies with scale from high correlation value to strongly anti-correlation value This studies is important because correlation coefficient is used to quantify degree of independence between two va…
The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family (˝r;g) of self-adjoint elliptic differential operators. (˝r;g) is a non-Laplace-type perturbation …
Guts determine the leading coefficients of L2-Alexander torsions for 3-manifolds.
problem Determining the leading coefficient of L2-Alexander torsions for 3-manifolds. method Using a new criterion for the convergence of Fuglede-Kadison determinants and the work of Agol and Zhang on guts of 3-manifolds.
result The leading coefficient equals the relative L2-torsion of the guts associated to the cohomology class. Survey of recent measures of association, including a new coefficient.
problem Exploring new measures of association in statistics.
method Survey and introduction of a new correlation coefficient.
result Proposed a new extension of the correlation coefficient to standard Borel spaces.