Related papers: Intersection Theory, Integrable Hierarchies and To…
The present paper deals with N=1 2D supersymmetric integrable quantum field theory. The S-matrix proposed to describe the interactions between supersymmetric particles is applied to theories involving topological excitations of zero central…
Using the connection between intersection theory on the Deligne-Mumford spaces and the edge scaling of the GUE matrix model (see math.CO/9903176, math.AG/0101147), we express the n-point functions for the intersection numbers as…
The aim of this paper is to study class number relations over function fields and the intersections of Hirzebruch-Zagier type divisors on the Drinfeld-Stuhler modular surfaces. The main bridge is a particular "harmonic" theta series with…
We obtain a simple, recursive presentation of the tautological (\kappa, \psi, and \lambda) classes on the moduli space of curves in genus zero and one in terms of boundary strata (graphs). We derive differential equations for the generating…
Moduli spaces of algebraic curves and closely related to them Hurwitz spaces, that is, spaces of meromorphic functions on the curves, arise naturally in numerous problems of algebraic geometry and mathematical physics, especially in…
We reformulate and motivate AKSZ-type topological field theories in pedestrian terms, explaining how they arise as the most general Schwartz-type topological actions subject to a simple constraint, and how they generalize Chern$-$Simons…
We consider the deformations of ``monomial solutions'' to Generalized Kontsevich Model \cite{KMMMZ91a,KMMMZ91b} and establish the relation between the flows generated by these deformations with those of $N=2$ Landau-Ginzburg topological…
Some new developments in constrained Lax integrable systems and their applications to physics are reviewed. After summarizing the tau function construction of the KP hierarchy and the basic concepts of the symmetry of nonlinear equations,…
The integrable structure of open--closed string theories in the $(p,q)$ conformal minimal model backgrounds is presented. The relation between the $\tau$--function of the closed string theory and that of the open--closed string theory is…
The principal goal of the paper is to apply the approach inspired by the theory of integrable systems to construct explicit sections of line bundles over the combinatorial model of the moduli space of pointed Riemann surfaces based on…
A $d$-dimensional invertible topological field theory is a functor from the symmetric monoidal $(\infty,n)$-category of $d$-bordisms (embedded into $\mathbb{R}^\infty$ and equipped with a tangential $(X,\xi)$-structure) which lands in the…
The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum version of the monodromy matrix…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
In arXiv:hep-th/0310113 we started a program of creating a reference-book on matrix-model tau-functions, the new generation of special functions, which are going to play an important role in string theory calculations. The main focus of…
This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…
Standard combinatorial construction, due to Kontsevich, associates to any $\ai$-algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We propose an…
It is well-known that the algebra of vector fields on the circle acts on the space of Riemann surfaces with a marked point and a local parameter at this point. We show that this action has a natural realization in the soliton theory, indeed…
The matrix model of topological field theory for the moduli space of p-th spin curves is extended to the case of the Lie algebra of the orthogonal group. We derive a new duality relation for the expectation values of characteristic…
We construct an elementary, combinatorial kind of topological quantum field theory, based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of…
The decomposition into interaction subspaces is a hierarchical decomposition of the spaces of cylindrical functions of a finite product space, also called factor spaces. It is an important construction in graphical models and a standard way…