Related papers: A Caporaso-Harris type Formula for relative refine…
A Fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine-invariance and implies the sharp $L^p-L^q$ restriction…
A metrized complex of algebraic curves is a finite metric graph together with a collection of marked complete nonsingular algebraic curves, one for each vertex, the marked points being in bijection with incident edges. We establish a…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.
The purpose of this paper is to list the refined Humbert invariants for a given automorphism group of a curve $C/K$ of genus 2 over an algebraically closed field $K$ with characteristic $0$. This invariant is an algebraic generalization of…
It has been proposed recently that topological A-model string amplitudes for toric Calabi-Yau 3-folds in non self-dual graviphoton background can be caluculated by a diagrammatic method that is called the ``refined topological vertex''. We…
This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…
The universal invariant with respect to a given ribbon Hopf algebra is a tangle invariant that dominates all the Reshetikhin-Turaev invariants built from the representation theory of the algebra. We construct a canonical strict monoidal…
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…
We study the quantum Riemann-Hilbert problems determined by the refined Donaldson-Thomas theory on the resolved conifold. Using the solutions to classical Riemann-Hilbert problems by Beidgeland, we give explicit solutions in terms of…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
We prove a family of factorization formulas for the combinatorial Donaldson--Thomas invariant for an acyclic quiver. A quantum dilogarithm identity due to Reineke, later interpreted by Rimanyi by counting codimensions of quiver loci, gives…
We define a signed count of real rational pseudo-holomorphic curves appearing in a one-parameter family of real Spin symplectic K3 surfaces. We show that this count is an invariant of the deformation class of the family. In the case of a…
Recent work of Kass--Wickelgren gives an enriched count of the $27$ lines on a smooth cubic surface over arbitrary fields. Their approach using $\mathbb{A}^1$-enumerative geometry suggests that other classical enumerative problems should…
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd dimensional manifold. Further, we calculate the…
The Welschinger invariants of real rational algebraic surfaces are natural analogues of the genus zero Gromov-Witten invariants. We establish a tropical formula to calculate the Welschinger invariants of real toric Del Pezzo surfaces for…
A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which…
We present theorems which provide the existence of invariant whiskered tori in finite-dimensional exact symplectic maps and flows. The method is based on the study of a functional equation expressing that there is an invariant torus. We…