Related papers: The Kontsevich integral
We present an elliptic version of Selberg's integral formula.
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb R}^n$ is established. The valuations obtained are functional versions of the…
This note presents selected values of definite integrals whose integrand contains a power of the Dedekind function having imaginary argument.
Invited contribution to the inaugural issue of {\em Physics Educator.}
Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.
We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic…
We generalize several integrals studied by Glaisher. These ideas are then applied to obtain an analog of an integral due to Ismail and Valent.
In this note we reconsider a familiar result in Vassiliev knot theory - that the coefficients of the Alexander-Conway polynomial determine the top row of the Kontsevich integral - from the point of view of Kazuo Habiro's clasper theory. We…
This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850
We study the integral transform which appeared in a different form in Akhiezer's textbook "Lectures on Integral Transforms".
This version has been withdrawn. The new and final version is on ArXiv 1103.4878
We generalize the definition of the framed Kontsevich integral initially presented by T.Q.T.Le and J.Murakami. We define an isotopy invariant $\widetilde{Z}_f$ that behaves well under band sum moves.
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
We explore some integrals associated with the Riesz function and establish relations to other functions from number theory that have appeared in the literature. We also comment on properties of these functions.
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
This is a survey on Sarnak's Conjecture
This is a detailed answer to the criticism of my paper.
The aim of this paper is to provide an overview of the results about classification of quantum groups that were obtained in arXiv:1303.4046 [math.QA] and arXiv:1502.00403 [math.QA].
This note contains my response to the comment written by J. Franklin on my paper ``Covariant formulation of electrodynamics in isotropic media''.