相关论文: The Kontsevich integral

This Paper (one first and draft version) contains some small imperfections, one its correct and definitive version has been already submitted to one prestigious review of mathematics. More precisely "the Special Function SHIN, II" will be…

This is a survey describing recents developments in enumerative geometry of curves on projective varieties. Various methods to arrive at results such as Kontsevich's formula for plane rational curves, or Caporaso-Harris's formula for plane…

The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…

This is a significant revision of the early version of this paper which was posted last December. The speculative section has been removed in light of some recent results of Morita and Kawazumi. Numerous typos have been fixed. The companion…

The paper is an introduction to intuitionistic mathematics.

Vassiliev's knot invariants can be computed in different ways but many of them as Kontsevich integral are very difficult. We consider more visual diagram formulas of the type Polyak-Viro and give new diagram formula for the two basic…

A concise introduction to the Standard Model of fundamental particle interactions is presented.

We compute the weight of a Kontsevich graph in deformation quantization. Up to rationals, the result is Zeta(3)^2/Pi^6.

This is a Reply to a Comment by V.P. Torchigin and A.V. Torchigin, published in Physical Review A 92, 017803 (2015). The paper which is commented upon is titled "Deducing radiation pressure on a submerged mirror from the Doppler shift,"…

This paper outlines a variety of possible applications of the Vlasov equation and its generalization, i.e., the Klimontovich equation, in various areas of many-body physics. In particular, these equations are shown to be used in…

We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.

This note is an (exact) copy of the report of Jaak Peetre, "Generalizing Ovchinnikov's Theorem". Published as Technical Report, Lund (1981). Some more recent general references have been added, some references updated though (in italics)…

Contents: Introduction(3).The method of Ermakov(4).The method of Milne(7). Pinney's result(8).Lewis' results(8). The interpretation of Eliezer and Gray(14). The connection of the Ermakov invariant with N\"other's theorem(17). Possible…

In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.

By employing polynomial-reduced KP integrability, combined with the string equation, this work establishes explicit relationships between the generalized Kontsevich model, the topological recursion of the spectral curve, and the geometry of…

The Kontsevich integral of a knot is a powerful invariant which takes values in an algebra of trivalent graphs with legs. Given a Lie algebra, the Kontsevich integral determines an invariant of knots (the so-called colored Jones function)…

Forty articles have been recently published in EPJD as contributions to the topical issue "Theory and applications of the Vlasov equation". The aim of this topical issue was to provide a forum for the presentation of a broad variety of…

The theory of intrinsic volumes of convex cones has recently found striking applications in areas such as convex optimization and compressive sensing. This article provides a self-contained account of the combinatorial theory of intrinsic…

We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched…

In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double…