A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Formula calculates knot Floer complexes for specific cable knots.
New subgroup found in knot homology concordance group.
Researchers describe a new Thom form for mapping cones.
Paper constructs Thom-Smale complex using instantons from Morse functions.
Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.
Novel Morse theory for mapping cone cohomology.
New non-existence results for harmonic maps into perturbed cones.
Paper proves unique tangent maps for complex maps into algebraic varieties.
The authors study in detail new types of varieties with degenerate Gauss maps: varieties with multiple foci and their particular case, the so-called twisted cones. They prove an existence theorem for twisted cones and describe their structure.
Extends knot invariant to filtered grid complexes.
We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive genus, when the target has conic points with cone angles less than . For a cone point of cone angle less than or equal we show that one can minimize, uniquely, in the relative hom…
We analyze errors in filtering algorithms using optimal transport.
Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the prepotential of the special Kahler geometry.
In this paper, we consider a natural map from the Kahler cone to the balanced cone of a Kahler manifold. We study its injectivity and surjecticity. We also give an analytic characterization theorem on a nef class being Kahler.
Using the mapping cone of a rational surgery, we give several obstructions for Seifert fibered surgeries, including obstructions on the Alexander polynomial, the knot Floer homology, the surgery coefficient and the Seifert and four-ball genus of the knot.
A new method improves Bayesian filtering in nonlinear systems.
Let be a connected, non-compact -dimensional Riemannian manifold. In this paper we consider smooth maps with images inside a non-degenerate cone. Under quite general assumptions on , we provide a lower bound for the width of the cone in terms of the energy and the tension of and a …
New cones in 4D space found with minimal mass.
The paper studies translation lengths on sphere complexes and related cones.
The main goal of this paper is a detailed study of asymptotic cones of the mapping class groups. In particular, we prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real trees, sending limits of hierarchy paths onto geodesics, and with image a median su…
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
The paper studies mapping class group actions on character varieties of surfaces.
We establish the existence of an integer degree for the natural projection map from the space of parameterizations of asymptotically conical self-expanders to the space of parameterizations of the asymptotic cones when this map is proper. As an application we show that there is an open set in the space of cones in the …
A new ensemble filter uses transport maps and MMD optimization for high-dimensional data assimilation.
Flexible metrics found on a genus 2 surface.
Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental non-expansiveness property of filtering maps in the space of probability distrib…
The uninformative ordering of artificial neurons in Deep Neural Networks complicates visualizing activations in deeper layers. This is one reason why the internal structure of such models is very unintuitive. In neuroscience, activity of real brains can be visualized by highlighting active regions. Inspired by those te…
We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal deformations of this complex manifold. By use of this map, we generalize an extension formula in a recent work of K. Liu, X. Yang and the first author. As direct corollar…
We show that the cone associated with a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be consider…
Bounded symmetric domains are biholomorphic to tube domains over Finsler symmetric cones.
We prove that tangent cones to 2-dimensional calibrated cycles are unique. Using this result we prove a rate of convergence for the mass of the blow-up of a calibrated integral 2-cycle towards the limiting density. With the same techniques, we can also prove such a rate for J-holomorphic maps between almost complex man…
New Calabi-Yau metrics constructed with detailed geometry at infinity.
In this article, we reformulate the cobordism map of embedded contact homology, which is induced by exact symplectic cobordism and defined as direct limit of homomorphisms called filtered ECH cobordism map. The filtered ECH cobordism map is defined by counting embedded holomorphic curves with zero ECH index and we prov…
In this article I show that every special Lagrangian cone in C^3 determines, and is determined by, a primitive harmonic surface in the 6-symmetric space SU_3/SO_2. For cones over tori, this allows us to use the classification theory of harmonic tori to describe the construction of all the corresponding special Lagrangi…
We show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and the boundary of surface meets the boundary of the cone with a constant angle, is radially graphical if the mean curvature is non-positive with respect to the Gauss map pointing toward the domain bounded by the surf…
The paper studies horofunction compactifications of symmetric cones under Finsler distances.
New distances for comparing multivariate normal distributions.
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated with differential elliptic complexes. Algebraically, we show that the filtered co…
The Gaiotto locus for Sp(2n) is shown to lie in the nilpotent cone.
This is the sixth in a series of papers constructing examples of special Lagrangian m-folds in C^m. We present a construction of special Lagrangian cones in C^3 involving two commuting o.d.e.s, motivated by the first two papers of the series. Then we generalize it to a construction of non-conical special Lagrangian 3-f…
Lawson-Osserman constructed three types of non-parametric minimal cones of high codimensions based on Hopf maps between spheres, which correspond to Lipschitz but non-differentiable solutions to the minimal surface equations, thereby making sharp contrast to the regularity theorem for minimal graphs of codimension 1. I…
Do and Norbury found a so-called differential relation which relates the volume of the moduli space of singular surface with a cone point to that of a smooth surface obtained by forgetting the cone point. Their procedure is valid for cone angles less than by work of Tan, Wong and Zhang. We study the moduli space of…
This paper proves area-minimizing cones over Grassmannian manifolds.
The first purpose of this note is to comment on a recent article of Bursztyn, Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of a manifold V, then there is a bijection between germs of tubular neighborhoods of M and germs of "Euler-like" vector fields on V. We shall explain how to approach…
dboost optimizes prediction models for convex cone problems.
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
The invariant measured foliations of a pseudo-Anosov homeomorphism induce a natural (singular) Sol structure on mapping tori of surfaces with pseudo-Anosov monodromy. We show that when the pseudo-Anosov has orientable foliations and does not have 1 as an eigenvalue of the induced cohomology action on…
We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show th…