Develops a new framework for temporal anchoring in deep embedding spaces.
problem Temporal anchoring in deep embedding spaces, especially drift and convergence issues.
method Operator-theoretic framework with drift maps and event-indexed blocks, proving convergence theorems and equivalence theorems.
result Proves convergence theorems and equivalence theorems for the proposed framework.
Index difference on surfaces of genus at least 3 is non-trivial.
problem Index difference on surfaces of genus at least 3
method Show that the index difference is non-trivial
result Index difference is non-trivial
This study compares microscopic and macroscopic models for commodity index derivatives pricing.
problem Lack of accurate futures curve dynamics in macroscopic models for real scenarios.
method Calibrated both microscopic and macroscopic models using S\&P GSCI Crude Oil excess-return index derivatives.
result Macroscopic models struggle to capture futures curve dynamics, affecting pricing and sensitivities.
Model prices commodity futures and index options.
problem Deriving accurate prices for derivative contracts on commodity futures and indices.
method Stochastic local volatility model for commodity futures.
result Model accurately recovers prices of derivative claims.
Reproduces basic supersymmetric QFTs using complexified graded algebraic geometry.
problem Understanding and describing supersymmetric quantum field theories.
method Tower construction in complexified Z/2-graded C-infinity-algebraic geometry and a purge-evaluation/index-contracting map.
result Reproduces d=3+1, N=1 Wess-Zumino model and U(1) gauge theory. New proof for hyperbolic groups using contracting boundaries of cusped spaces.
problem Proving groups are hyperbolic relative to subgroups.
method Proving compact contracting boundary of cusped space implies hyperbolicity.
result If cusped space Gh has compact contracting boundary, then G is hyperbolic relative to subgroups H. The study shows that certain complex geometries are hyperbolic and contractible but fail to be CAT(0).
problem The failure of certain complex geometries to be CAT(0) despite being hyperbolic and contractible.
method The study uses combinatorial methods to demonstrate the failure of these geometries to satisfy a combinatorial isoperimetric inequality.
result The study proves that these geometries, while hyperbolic and contractible, do not satisfy a combinatorial isoperimetric inequality.
Study on contracting maps and their rigidity under curvature constraints.
problem Rigidity of contracting maps between manifolds with positive curvature.
method Analysis of curvature pinching and contracting conditions involving singular values.
result Established the relation between curvature pinching and contracting conditions.
Mapping class groups of Haken 3-manifolds enjoy many of the homological finiteness properties of mapping class groups of 2-manifolds of finite type. For example, H(M) has a torsionfree subgroup of finite index, which is geometrically finite (i. e. is the fundamental group of a finite aspherical complex). This was prove…
In a previous paper, we showed nonvaninishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from the first relevant paper of Gromov and Lawson, involving contracting maps defined on …
The study of double coset growth in specific groups confirms a conjecture about generic 3-manifolds.
problem Understanding the growth of double cosets in specific groups.
method Generalizing previous work on hyperbolic groups, the study proves the growth of double cosets for certain subgroups.
result The double coset growth of certain subgroups is comparable to the orbital growth function.
The paper proves scalar curvature decay for uniformly contractible manifolds with finite asymptotic dimension.
problem Proving decay of scalar curvature for uniformly contractible manifolds with finite asymptotic dimension.
method Using index pairing between Dirac operators and compactly supported vector bundles with Lipschitz control, and Lipschitz control for topological K-theory of finite dimensional simplicial complexes.
result The scalar curvature decays to zero at a rate depending only on the contractibility radius and the diameter control of the asymptotic dimension.
Formula found for skinning map contraction in hyperbolic geometry.
problem Finding the contraction constant of skinning maps.
method Elementary hyperbolic geometry and moduli spaces of hyperbolic manifolds.
result Explicit formula for contraction constant.
We will show that for a polynomially contractible manifold of bounded geometry and of polynomial volume growth every coarse and rough cohomology class pairs continuously with the K-theory of the uniform Roe algebra. As an application we will discuss non-vanishing of rough index classes of Dirac operators over such mani…
In this paper, we prove that for every irreversible Finsler n-dimensional real projective space (RPn,F) with reversibility λ and flag curvature K satisfying 916(1+λλ)2<K≤1 with λ<3, there exist at least n−1 non-contractible closed geodesics. In addition, if the met…
Maps from spheres and disks to convex shapes via curvature flow.
problem Constructing contractions from spheres and disks to convex shapes.
method Inverse mean curvature flow to create normalized-area-preserving contractions.
result Proves E. Milman's conjecture and gives spectral comparison results.
New method computes contact invariants for non-simply connected Gorenstein toric contact manifolds.
problem Computing contact invariants for non-simply connected Gorenstein toric contact manifolds.
method Using moment map data and Conley-Zehnder index to compute invariants for non-contractible periodic Reeb orbits.
result Explicit computation of contact invariants for specific examples of Gorenstein contact lens spaces.
We prove exponential growth rate of contractible closed geodesics for an arbitrary bumpy metric on manifolds of the form X#Y, where the fundamental group of X has a subgroup of finite index at least 3 and Y is simply connected and not a homotopy sphere.
Injectivity of fundamental group map proves contractibility of intersection in CAT(0) complexes.
problem Proving contractibility of intersections of subcomplexes in non-positively curved 2-complexes.
method Injectivity of the induced map from fundamental groups.
result Each component in the intersection of two contractible subcomplexes in a CAT(0) 2-complex is contractible.
New rigidity result for maps between curved spaces.
problem Rigidity of contracting maps between curved manifolds.
method New long-time existence of harmonic map heat flow.
result Distance non-increasing maps are either submersion or isometry under certain conditions.
Uniformly extend maps on Hadamard manifolds with curvature constraints.
problem Extending maps on Hadamard manifolds with curvature constraints.
method Proving uniform extension for contracting maps on Hadamard manifolds with curvature bounds.
result Uniform Lipschitz extension achieved for contracting maps on Hadamard manifolds with curvature constraints.
Study analyzes fees linked to VIX index in annuity contracts.
problem Impact of VIX-linked fees on annuity contract surrender strategies.
method Two-layer continuous-time Markov chain approximation for fund value process.
result Optimal surrender strategy is more robust to VIX-linked fees.
Nearly spherical, positively curved surfaces are mapped from a sphere.
problem Mapping nearly spherical, positively curved surfaces from a sphere.
method Combines Ricci flow, Kim-Milman construction, and Bakry-Émery criterion.
result Every nearly spherical, positively curved surface is the contractive image of a round sphere.
We present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in the edge graph of equivelar maps on surfaces. We also present an algorithm to construct such cycles. This is further generalized and shown to hold for more general maps.
This study examines lead-lag relationships in Chinese futures markets using high-frequency data.
problem Understanding high-frequency trading dynamics and information flow in futures markets.
method High-frequency tick-by-tick data analysis of lead-lag relationships between different maturity futures contracts.
result The near-month futures lead longer-dated contracts by one tick, with a negative feedback effect on the leading asset.
Groups can embed uniformly but not act properly on contractible manifolds.
problem Understanding the difference between group actions and embeddings on contractible manifolds.
method Analyzing the relationship between group actions and uniform embeddings on contractible manifolds.
result k-fold products of specific groups do not act on contractible manifolds.
We present a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of contractible Hamiltonian cycle in equivelar triangulated maps. We also present an alg…
We establish multiplicity results for geometrically distinct contractible closed Reeb orbits of non-degenerate contact forms on a broad class of prequantization bundles. The results hold under certain index requirements on the contact form and are sharp for unit cotangent bundles of CROSS's. In particular, we generaliz…
The paper refines the three-page index for links, proving a new bound and characterizing specific links.
problem Investigating the three-page index invariant for links and proving bounds.
method Constructing three-page presentations from reduced link diagrams via binding circles and contractible subcomplexes.
result Proves a new bound for the three-page index and characterizes links achieving equality.
The paper studies cohomology of groups with contracting elements.
problem Understanding the cohomology of groups with specific elements.
method Proving infinite-dimensional relative bounded cohomology for groups with contracting elements.
result The cohomology is infinite-dimensional for groups with contracting elements.
A new clustering framework using fixed points for data analysis.
problem Lack of unified understanding and application of clustering algorithms in data analysis.
method Restated model-based clustering using fixed point theory, iteratively constructing contraction maps to find cluster centers.
result Unified clustering framework reveals convergence mechanisms and interconnections among clustering algorithms.
In this paper we propose a multi-state model for the evaluation of the conversion option contract. The multi-state model is based on age-indexed semi-Markov chains that are able to reproduce many important aspects that influence the valuation of the option such as the duration problem, the time non-homogeneity and the …
Deviation inequalities and limit laws for random walks on metric spaces.
problem Understanding random walks on metric spaces with contracting isometries.
method Adapting Gouëzel's pivotal time construction to establish deviation inequalities.
result Exponential bounds and limit laws for random walks on mapping class groups and CAT(0) spaces.
Analyzes complex structure deformations using cohomology contraction methods.
problem Deforming complex structures and identifying obstructions.
method Refined power series method for (p,q)-forms and complex structures, using Frölicher spectral sequence. result All obstruction classes lie in the kernel of contraction maps under natural vanishing conditions.
Low-index harmonic maps from S3 to S2 are simple.
problem Characterizing harmonic maps with low Morse index.
method Proving any such map is an isometry, fibration, and holomorphic composition.
result Harmonic maps of low index are restricted to specific compositions.
We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other and is invariant by topological conjugacies that preserve orientation. We prove…
The paper bounds the energy index of harmonic Gauss maps on surfaces.
problem Bounding the energy index of harmonic Gauss maps on surfaces.
method Analyzes closed and complete non-compact surfaces in Lie groups with bi-invariant metrics.
result The energy index of the Gauss map is bounded by the topological genus.
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.
Proves existence and uniqueness of mean curvature flow.
problem Existence and uniqueness of mean curvature flow.
method Heat kernel estimates and contraction mapping principle.
result Continuous dependence of mean curvature flow on initial data.
Local constancy of index for certain gradient mappings proved.
problem Proving the local constancy of the index for specific gradient mappings.
method Using a more general theorem for quasiregular gradient mappings, deducing the result from the Hessian's properties.
result The index is locally constant for C1,1 functions with uniformly positive determinant Hessian almost everywhere. We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely generated, non-elementary group G acting on a G--space X, we prove that if G contains a strongly contracting eleme…
Researchers found counterexamples to conjectures about optimal transport maps on curved spaces.
problem Extending Caffarelli's contraction theorem to curved spaces.
method Constructing counterexamples to precise conjectures.
result Found counterexamples to Milman's conjectures about optimal transport maps on curved spaces.
The compact curves of an intermediate Kato surface S form a basis of H2(S,Q). We present a way to compute the associated rational coefficients of the first Chern class c1(S). We get in particular a simple geometric obstruction for c1(S) to be an integral class, or equivalently index(S)=1. We also f…
We propose the use of statistical emulators for the purpose of valuing mortality-linked contracts in stochastic mortality models. Such models typically require (nested) evaluation of expected values of nonlinear functionals of multi-dimensional stochastic processes. Except in the simplest cases, no closed-form expressi…
Paper constructs a transfer map for codimension 2 submanifolds in higher index theory.
problem Higher index theory of codimension 2 submanifolds.
method Construction of codimension 2 transfer map and adjoint relationship with cyclic cohomology.
result Established adjoint relationship between codimension 2 transfer map and co-transfer map in cyclic cohomology.
Paper proves existence of Dirac-harmonic maps with trivial index.
problem Finding Dirac-harmonic maps with trivial index.
method Defining a new quantity and proving its homotopy invariance.
result Existence of Dirac-harmonic maps from closed Riemann surfaces to Kähler manifolds.
Study describes index map for a specific algebra of pseudodifferential operators.
problem Understanding the K-theory index map for a particular algebra of pseudodifferential operators.
method Description of the K-theory index map associated with the continuous extension of the principal-symbol map.
result The index map takes values in K_0 of the commutator ideal E, which is isomorphic to Z^2.
New theorem shows nearly spherical manifolds can be mapped from spheres.
problem Generalizing Caffarelli's theorem to nearly spherical manifolds.
method Optimal transport map on the sphere, stability result.
result Every nearly spherical manifold can be mapped from a sphere.