Related papers: Simple Formulas for Generating Chern-Simons Basic …
Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of…
We construct Gromov-Witten invariants of general symplectic manifolds.
In this paper, we derive eight basic identities of symmetry in three variables related to generalized Euler polynomials and alternating generalized power sums. All of these are new, since there have been results only about identities of…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms…
We investigate a strong coupling expansion of N=6 superconformal Chern-Simons theory obtained from the semiclassical analysis of low energy, effective degrees of freedom given by the eigenvalues of a certain matrix model. We show how the…
Chern-Simons theories, which are topological quantum field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of quantum field theories which can be exactly and…
After a brief description of the $\mathbb{Z}$-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
A construction of algebraic surfaces based on two types of simple arrangements of lines, containing the prototiles of substitution tilings, has been proposed recently. The surfaces are derived with the help of polynomials obtained from…
We search for vortices in a generalized Abelian Chern-Simons model with a nonstandard kinetic term. We illustrate our results, plotting and comparing several features of the vortex solution of the generalized model with those of the vortex…
We explain how to determine equations describing the ramification of an outer simple linear projection of a projective scheme in a way suited for explicit computations.
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
We construct an invariant of 3-manifolds using a modification of the Kontsevich integral and Kirby's calculus. This invariant, as expected in perturbative Chern-Simon theory, takes values in the algebra of oriented 3-valent graphs. This…
A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice…
We give a simple proof of an explicit formula for Kerov polynomials. This formula is closely related to a formula of Goulden and Rattan.
We present a gluing formula for Gromov-Witten invariants in the case of a triple product. This gluing formula is a simple case of a much more general gluing formula proved and stated using exploded manifolds. We present this simple case…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
We prove a wall crossing formula of Donaldson-Thomas type invariants without Chern-Simons functionals.
The roots of any polynomial of degree m with complex integer coefficients can be computed by manipulation of sequences made from distinct symbols and counting the different symbols in the sequences. This method requires only primitive…