Study introduces new indices for special fibered surfaces of genus 4.
problem Characterizing relatively minimal fibered surfaces of genus 4.
method Introduces Horikawa index and local signature for surfaces with unique trigonal structure.
result New indices provide insights into the structure of surfaces.
Classifies normal stable Horikawa surfaces with smoothable singularities.
problem Characterizing surfaces with specific singularities and smoothability criteria.
method Classification and smoothability criterion based on log canonical singularities.
result Provides a criterion for global Q-Gorenstein smoothability of Horikawa surfaces. We calculate the monodromies of the canonical Lefschetz pencils on a pair of homeomorphic Horikawa surfaces. We show in particular that the (pluri)canonical pencils on these surfaces have the same monodromy groups, and are related by a "partial twisting" operation.
In this article we prove that Fintushel-Stern's construction of Horikawa surface, which is obtained from an elliptic surface via a rational blow-down surgery in smooth category, can be performed in complex category. The main technique involved is Q-Gorenstein smoothings.
Classifies surfaces with T-singularities and ample canonical class.
problem Classifying surfaces with T-singularities and specific properties.
method Using KSBA moduli space and techniques for surfaces with T-singularities.
result Identifies surfaces with only T-singularities in the KSBA space and proves non-smoothability conditions.
In this paper, we study deformations of holomorphic Poisson maps which extend Horikawa's series of papers on deformations of holomorphic maps in the context of holomorphic Poisson deformations. In appendices, we present deformations of Poisson morphisms in the language of functors of Artin rings which is the algebraic …
Study Kähler geometry on Hurwitz spaces of Riemann surfaces.
problem Curvature of Kähler metric on Hurwitz spaces.
method Generalized Weil-Petersson metric and Horikawa's deformation theory.
result Investigate curvature of Kähler metric on Hurwitz spaces.
Study tests if deep hedging differs from delta hedging in a GARCH market model.
problem Whether deep hedging includes speculative components in a GARCH market.
method Tested in a GARCH-based market model, comparing deep hedging and delta hedging.
result The difference between deep hedging and delta hedging is speculative if risk measure does not prioritize adverse outcomes.
Study complex curves in rational surfaces using bridge trisections.
problem Classifying and understanding complex curves in rational surfaces.
method Bridge trisections and branched covering operations.
result Any curve in CP2 or CP1imesCP1 admits an efficient bridge trisection. A new clustering evaluation index based on density estimation.
problem Improving internal clustering evaluation indices.
method The index is a mixture of Ambiguous and Similarity sub-indices, calculated using density estimation.
result The new index significantly outperforms other internal clustering evaluation indices.
Study on symmetric operators on non-compact manifolds, focusing on their index modulo 2.
problem Investigating elliptic operators with a specific symmetry and their index modulo 2.
method Analysis of Callias-type operators on non-compact manifolds, establishing mod 2 versions of index theorems.
result Established mod 2 versions of the Gromov-Lawson relative index theorem, Callias index theorem, and Boutet de Monvel's index theorem for Toeplitz operators.
New index formula connects numerical and K-theoretic indices.
problem Equivariant index for proper group actions on manifolds.
method Developed a trace on group conjugacy classes to relate numerical and K-theoretic indices. result Shows that numerical index equals K-theoretic index under certain conditions. New index connects Diederich-Fornæss index to boundary conditions.
problem Understanding the Diederich-Fornæss index for complex domains.
method Defined and proved new index equivalence; used complex geometric analytic techniques.
result First precise non-trivial Diederich-Fornæss index in Euclidean spaces.
The paper explores global index formulas for one-dimensional holomorphic foliations.
problem Global index formulas for one-dimensional holomorphic foliations.
method Microlocal point of view and short proofs for existing index formulas.
result Generalizations of existing index formulas.
CCI30 is a new cryptocurrency index.
problem None explicitly stated in the abstract.
method Not specified in the abstract.
result Not specified in the abstract.
Explain Arnold's proof of the Morse index theorem using Maslov index.
problem Proving the Morse index theorem in Riemannian geometry.
method Using symplectic arguments and the Maslov index.
result Self-contained exposition of Arnold's proof.
The p-index improves investment performance for NYSE stocks but not for SSE stocks.
problem Improving investment performance for stocks using the p-index.
method Comparing different p-ratio strategies and empirical efficient frontiers for SSE and NYSE stocks.
result The p-index enhances investment performance for NYSE stocks but not for SSE stocks.
Study Whittle index learning algorithms for restless bandits with constant stepsizes.
problem Optimizing decisions in restless multi-armed bandits with constant stepsizes.
method Developed Q-learning algorithms with constant stepsizes for index learning in restless bandits, extending to DQN and function approximations.
result The algorithms learn the Whittle index effectively.
Paper introduces danceability index as a new bridge index definition.
problem Defining the bridge index in various mathematical contexts.
method Proves danceability index as equivalent to bridge index, extends to virtual knots.
result Danceability index is a new equivalent definition of the bridge index.
Constructs index class for manifolds with group action.
problem Index class construction for manifolds with group action.
method Constructs coarse index class with support condition using equivariant Dirac operator.
result Shows coarse relative index theorem and compatibility with suspension isomorphism.
New techniques simplify computing geometric index of links in solid tori.
problem Computing the geometric index of links in solid tori.
method Introducing geometric index for solid chambers and proving its computation under specific conditions.
result Simplified computation of geometric index for new examples.
A new index rebalancing strategy reduces large constituent weights without undesirable effects.
problem Undesirable effects of current Nasdaq-100 index rebalancing.
method A simple rebalancing strategy that avoids undesirable effects.
result Preserves the order of index weights and prevents maximum weight increase.
Study on symmetric braid index of ribbon knots, deriving bounds and characterizations.
problem Understanding the symmetric braid index of ribbon knots.
method Defining symmetric braid index, using Khovanov homology, and calculating bounds.
result Existence of knots with symmetric braid index greater than braid index.
Study proves bridge and braid indices match for twist positive knots.
problem Determining when bridge and braid indices are equal for knots.
method Used knot Floer torsion order to prove for all twist positive knots.
result Bridge and braid indices coincide for all twist positive knots.
Minimal grid diagrams for 15,735 knots with 14 crossings and arc index 14.
problem Representing prime knots with 14 crossings and specific arc indices using grid diagrams.
method Enumerated all prime knots with 14 crossings, categorized by arc index, and found minimal grid diagrams for those with arc index 14.
result 8,027 knots with arc index 13 and 15,735 knots with arc index 14 were represented by minimal grid diagrams.
Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples th…
Proves the index of a Möbius band in 4D ball equals 5.
problem Determining the Morse index of critical non-orientable surfaces.
method Comparison theorem between Steklov spectral index and energy index.
result Proves the index of critical Möbius band in B4 equals 5. Enhanced indexation uses equity and index options for better performance.
problem Improving portfolio performance through enhanced indexation.
method Integrating index options into an enhanced indexation strategy based on second-order stochastic dominance.
result Introducing option strategies in enhanced indexation leads to improved out-of-sample performance.
Finite index subgroups of relatively hyperbolic groups have equal index.
problem Finite index subgroups of relatively hyperbolic groups have equal index.
method Demonstrating that the number of simplices in a simplicial classifying space grows linearly with index.
result Finite index subgroups of relatively hyperbolic groups have equal index.
The abstract discusses connecting quantum mechanics and algebraic index theories.
problem Exploring the connection between quantum mechanics and algebraic index theories.
method Explains how the classical algebraic index theorem can be proved in terms of BV quantization of topological quantum mechanics and 2d chiral CFT.
result Shows how the generating function of all genus Gromov-Witten invariants on elliptic curves is mirror equivalent to an elliptic chiral index.
Researchers construct an index map for contact manifolds using K-theory.
problem Constructing an index for maximally hypoelliptic operators on contact manifolds.
method Using Higson's construction for symbol class in K-theory, they derive a series of maps whose induced map in K-theory is the Heisenberg Atiyah-Singer index map.
result Explicit construction of a series of maps leading to the Heisenberg Atiyah-Singer index map.
Analyzes necessary and sufficient conditions for domains to have trivial Diederich-Fornæss index.
problem Understanding domains with trivial Diederich-Fornæss index in complex spaces.
method New geometric analysis method based on Riemannian geometry and de Rham cohomology.
result Analytical and geometric conditions for domains to have trivial index.
Deep learning predicts market sensitivities for cost-effective index tracking.
problem Costly and impractical replication of index funds.
method Learning to predict market sensitivities using deep learning models.
result Significant reduction in prediction errors compared to historical methods.
New index formula for hypoelliptic operators on manifolds.
problem Index computation for hypoelliptic differential operators.
method Generalized index formula for *-maximally hypoelliptic operators.
result Explicit index computations for Hormander's sum of squares operators.
Study on minimal surfaces with free boundary in a half-space, improving index estimates.
problem Non-existence of index two embedded minimal surfaces with free boundary in a half-space.
method Improved estimates of Neumann and Dirichlet indices, simplified proof of lower bounds.
result Answered Ambrozio et al.'s question and provided new lower bounds.
New theorem for manifolds with boundaries calculates operator index.
problem Calculating index of Callias-type operators on manifolds with boundaries.
method Combines indexes of induced operators on a compact hypersurface.
result Generalizes Callias-type index theorem to manifolds with compact boundaries.
An upper bound of the superbridge index of the connected sum of two knots is given in terms of the braid index of the summands. Using this upper bound and minimal polygonal presentations, we give an upper bound in terms of the superbridge index and the bridge index of the summands when they are torus knots. In contrast…
Listed 19,513 prime knots with arc index 12-16.
problem Tabulating prime knots with specific arc indices.
method Provided list of prime knots with minimal grid diagrams.
result 19,513 prime knots with arc index 12-16.
A new stock index model simplifies high-dimensional stock data.
problem Reflecting the overall stock market activity in high-dimensional data.
method Manifold learning and feature detection on discrete Laplace-Beltrami operator.
result The MF index series approximates the stock market better and has lower risk.
New method accurately reconstructs Russell 3000 index, revealing crowded portfolios.
problem Crowding in index portfolios during reconstitution events.
method Developed a Python package for accurate index reconstruction using CRSP US Stock data.
result Annual Russell 3000 portfolios are more crowded than quarterly ones, suggesting lower transaction costs.
Paper introduces unknotting index for virtual knots.
problem Computing and understanding virtual knots.
method Using writhe invariants and relationships with virtual knot module.
result Existence of virtual knots with specific unknotting indices.
In this paper we study the chord index of virtual knots, which can be thought of as an extension of the chord parity. We show how to use the chord index to define finite type invariants of virtual knots. The notions of indexed Jones polynomial and indexed quandle are introduced, which generalize the classical Jones pol…
Formula for Z_2-valued index of symmetric operators on manifolds.
problem Index of symmetric operators on manifolds with boundary.
method Cohomological formula for Z_2-valued index.
result A formula for the Z_2-valued index of operators on manifolds.
We introduce a notion of cobordism of Callias-type operators over complete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application we prove a gluing formula for Callias-type index. In particular, a usual index of an elliptic operator on a compact manifold can be computed as a s…
We study differential operators on complete Riemannian manifolds which act on sections of a bundle of finite type modules over a von Neumann algebra with a trace. We prove a relative index and a Callias-type index theorems for von Neumann indexes of such operators. We apply these results to obtain a version of Atiyah's…
Study estimates self-shrinker index with conical ends, proving index bound.
problem Estimating the index of self-shrinkers with asymptotically conical ends.
method Constructing Gaussian Harmonic forms and extending index estimates.
result Proves Morse index of self-shrinkers is at least (2g+r-1)/3.
Proves a lattice version of the Atiyah-Singer index theorem.
problem Index problems of Wilson-Dirac operators on lattice approximations of manifolds.
method Formulates and proves a K-theoretic formula for an index-type invariant. result Main theorem gives a formula for an index-type invariant of operators on lattice approximations of closed integral affine manifolds.
Bounds on the index of free boundary minimal surfaces.
problem Understanding the index of free boundary minimal surfaces.
method Comparison of energy and area indices, combining with previous work.
result Area index is bounded by a linear function of genus and boundary components.