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.
Research shows Upsilon function singularity location predicts algebraic knot genus.
Germs of Goursat distributions can be classified according to a geometric coding called an RVT code. Jean (1996) and Mormul (2004) have shown that this coding carries precisely the same data as the small growth vector. Montgomery and Zhitomirskii (2010) have shown that such germs correspond to finite jets of Legendrian…
Completing segments of a real tree doesn't yield a complete space.
This work improves interpretability and calibration of complex-valued neural networks using Newton-Puiseux analysis.
Suppose C is a singular curve in CP^2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots K_i. We apply Heegaard Floer theory to find new constraints on the sets of knots {K_i} that can arise as the links of singularities of cuspidal curves.…
Introduces new limit spaces for degenerating Calabi-Yau families.
Study uncovers complex critical points in tensor decomposition.
The level curves of an analytic function germ almost always have bumps at unexpected points near the singularity. This profound discovery of N. A'Campo is fully explored in this paper for $f(z,w)\in \C\{z,w\}$, using the Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac ph…
We give bounds on the gap functions of the singularities of a cuspidal plane curve of arbitrary genus, generalising recent work of Borodzik and Livingston. We apply these inequalities to unicuspidal curves whose singularity has one Puiseux pair: we prove two identities tying the parameters of the singularity, the genus…
We construct sequences of pseudo-Anosov mapping classes whose dilatations behave asymptotically like the inverse of the Euler characteristic of the surface they are defined on. These sequences are used to show that if the genus, g, and punctures, n, of a surface are related by a rational ray g=rn then the minimal dilat…
New method constructs small symplectic 4-manifolds via contact gluing.
Prime homology detects split links in prime characteristic.
A new model captures dependencies and unique characteristics in multi-dimensional sequences.
TREP learns pedestrian trajectories efficiently without needing full datasets.
Given a fibered link, consider the characteristic polynomial of the monodromy restricted to first homology. This generalizes the notion of the Alexander polynomial of a knot. We define a construction, called iterated plumbing, to create a sequence of fibered links from a given one. The resulting sequence of characteris…
Study of involutive monopole Floer homology and Khovanov homology in characteristic two.
We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah sequences associated to transversal tangential distributions.
We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results due to Guillemin and Quillen relating involutivity, restrictions, characteristics and characteristicity, known for first order systems, extend to the general context, though in a modifie…
Improved neural models for diverse user event sequences.
Establishes a spectral sequence linking instanton and Khovanov homologies.
The paper extends curvature concepts to surfaces in normed spaces.
FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the corresponding sequence of S_n-representations. In this paper we prove the Noetherian pro…
Classifies semi-equivelar gems on surfaces with Euler characteristic -1.
We establish two exact sequences for the lattice cohomology associated with non-degenerate plumbing graphs. The first is the analogue of the surgery exact triangle proved by Ozsvath and Szabo for the Heegaard-Floer invariant HF^+; for the lattice cohomology over Z_2-coefficients it was proved by J. Greene. Here we prov…
Researchers adapt Newstead's method to compute betti numbers in characteristic 2.
New homologies prove -holonomicity of knot polynomials.
Convolutional model disaggregates electricity consumption data.
Study shows link polynomial evaluations from Heegaard Floer theory.
Computes monopole Floer homology for three-manifolds.
Formula for Euler characteristic of moduli spaces of Abelian differentials.
Hybrid model combines RNNs, encoders-decoders, and Transformers for sequence tasks.
We proved the convergence of a sequence of 2 dimensional comapct Kahler-Einstein orbifolds with rational quotient singularities and with some uniform bounds on the volumes and on the Euler characteristics of our orbifods to a Kahler-Einstein 2-dimensional orbifold. Our limit orbifold can have worse singularities than t…
Spectral sequence links knot Floer homology to HOMFLY-PT polynomial.
Paper develops a statistical model for summarizing event sequences.
A new method learns noise characteristics for better state estimation in real-time systems.
Study reveals noise in signals made from nonoverlapping rectangular pulses.
We investigate Bar-Natan's characteristic two Khovanov link homology theory studying both the filtered and bi-graded theories. The filtered theory is computed explicitly and the bi-graded theory analysed by setting up a family of spectral sequences. The E_2-pages can be described in terms of groups arising from the act…
Seq-SetNet processes sequence sets directly, improving protein structure prediction.
For germs of subanalytic sets, we define two finite sequences of new numerical invariants. The first one is obtained by localizing the classical Lipschitz-Killing curvatures, the second one is the real analogue of the evanescent characteristics introduced by M. Kashiwara. We show that each invariant of one sequence is …
New spectral sequences link knot homology to instantons, revealing concordance invariants.
We investigate the geometric characteristics of constant gaussian curvature surfaces obtained from solutions of the sigma model. Most of these solutions are related to the Veronese sequence. We show that we can distinguish surfaces with the same gaussian curvature using additional quantities like the topologic…
The study compares different scRNA sequencing methods using a high-dimensional dataset.
New spectral sequence connects Khovanov homology to real monopole Floer homology.
Sequence Transformer Networks improve mortality prediction in clinical time-series data.
Paper shows odd Euler characteristic surfaces in hyperbolic 3-manifolds.
We give the first explicit computations of rational homotopy groups of spaces of "long knots" in Euclidean spaces. We define a spectral sequence which converges to these rational homotopy groups whose E^1 term is defined in terms of braid Lie algebras. For odd k we establish a vanishing line for this spectral sequence,…
We express characteristic numbers of compact hyperkähler manifolds in graph-theoretical form, considering them as a special case of the curvature invariants introduced by Rozansky and Witten. The appropriate graphs are generated by ``wheels'' and we use the recently proved Wheeling Theorem to give a formula for the L2 …
We define a renormalized characteristic class for Einstein asymptotically complex hyperbolic (ACHE) manifolds of dimension 4: for any such manifold, the polynomial in the curvature associated to the characteristic class euler-3signature is shown to converge. This extends a work of Burns and Epstein in the Kahler-Einste…