Related papers: Maslov index formulas for Whitney n-gons
We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new…
This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are…
In this paper we prove a residue formula for intersection pairings of reduced spaces of certain quasi-Hamiltonian G-spaces, by constructing the corresponding Hamiltonian G-space. Our argument closely follows the methods of a 1998 paper of…
Given a hypersurface $i \colon X \hookrightarrow \widetilde{P}^n$ in a weighted projective space, we compute the intersection form on the second cohomology $H^2(X, \mathbb{Z})^{\otimes n-1} \to \mathbb{Z}$ for the purpose of identifying…
We provide a formula for the partition function of five-dimensional $\mathcal{N}=1$ gauge theories on $\mathcal{M}_4 \times S^1$, topologically twisted along $\mathcal{M}_4$ in the presence of general background magnetic fluxes, where…
We will discuss a method for visual presentation of knotted surfaces in the four space, by examining a number and a position of its Morse's critical points. Using this method, we will investigate surface-knot with one critical point of…
We explicitly compute the diverging factor in the large genus asymptotics of the Weil-Petersson volumes of the moduli spaces of $n$-pointed complex algebraic curves. Modulo a universal multiplicative constant we prove the existence of a…
We give a simple formula for the signature of a foldable triangulation of a lattice polygon in terms of its boundary. This yields lower bounds on the number of real roots of certain of systems of polynomial equations known as "Wronski…
In this note the interrelations between several natural morphisms on the $\pi_1$ of groups of Hamiltonian diffeomorphisms are investigated. As an application, the equality of the (non-linear) Maslov index of loops of quantomorphisms of…
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in…
A regular $n$-gon inscribing a knot is a sequence of $n$ points on a knot, such that the distances between adjacent points are all the same. It is shown that any smooth knot is inscribed by a regular $n$-gon for any $n$.
The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and…
New formulas for the nth moment of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A…
Geometric products on tensor powers $\Lambda(V)^{\otimes m}$ of an exterior algebra and on Whitney algebras \cite{crasch} provide a rigorous version of Grassmann's {\it regressive products} of 1844 \cite{gra1}. We study geometric products…
We prove that Hofer's distance between two diameters of the open 2-disk admits an upper bound in terms of the Maslov index of their intersection points.
This note presents a formula for the enumerative invariants of arbitrary genus in toric surfaces. The formula computes the number of curves of a given genus through a collection of generic points in the surface. The answer is given in terms…
An effective method of computing division polynomials in terms of Mumford coordinates is presented. As an example, division polynomials for $3$- and $4$-torsion divisors on a genus two curve are obtained explicitly in terms of Mumford…
In this paper, using the formula for the integrals of the $\psi$-classes over the double ramification cycles found by S. Shadrin, L. Spitz, D. Zvonkine and the author, we derive a new explicit formula for the $n$-point function of the…
We propose an algorithm based on Newton's method and subdivision for finding all zeros of a polynomial system in a bounded region of the plane. This algorithm can be used to find the intersections between a line and a surface, which has…
We discover that tautological intersection numbers on $\bar{\mathcal{M}}_{g, n}$, the moduli space of stable genus $g$ curves with $n$ marked points, are evaluations of Ehrhart polynomials of partial polytopal complexes. In order to prove…