Analysis of mathematical works of A.G. Kostyuchenko.

Teichmüller theory is a ramified and rapidly developing area of mathematics which has multiple connections with other directions in the mathematical sciences and with their applications, first and foremost in mathematical physics. In this survey the main lines of development of this theory and its applications to string theory are presented in a historical context. Bibliography: 128 titles.

In this paper we prove the indicated conjecture in the last case of known infinite series of theta-blocks of weight 2.

Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians in terms of the current generators of the Yangian double . The method of projections onto intersections of different types of Borel subalgebras of this infinite-dimensional algebra is used to construct the Bethe vectors. Calculation of these projections makes it possible to express the supersymmetric Bethe vectors in terms of the matrix elements of the universal monodromy matrix. Two different presentations for the Bethe vectors are obtained by using two different but isomorphic current realizations of the Yangian double . These Bethe vectors are also shown to obey certain recursion relations which prove their equivalence.

New results on distributions of polynomials on multidimensional and infinite-dimensional spaces with measures are obtained

We prove that a right-continuous integrable stochastic process admits a minimal embedding in the standard Brownian motion if and only if it is a submartingale or supermartingale.

This is a survey article on Morse-Smale cascades on orientable 3-manifolds. It contains results of the authors and their collaborators on topological classication, the relation of dynamics with the topology of the ambient manifold, criteria for embeddability in a topological ow and a sucient and necessary condition for the existence of an energy function for the cascades.

This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical results established for isomonodromic deformations of Fuchsian systems are generalized to the case of integrable deformations of meromorphic systems. Bibliography: 40 titles.

In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed.

The paper deals with the problem of finding the probability threshold for the existence of a panchromatic colouring for a random hypergraph in the binomial model.

We prove that any distribution on the positive half-line with infinite expectation can be a distribution of the terminal value of an increasing process such that the difference between the terminal values of its compensator and the increasing process itself is 1.