Doctor of mathematics (1974). Professor of the Chair of higher geometry and topology of the Department of Mathematics and Mechanics of MSU (1979). Leading researcher of the Steklov mathematical institute of RAS.

Member of Moscow mathematical society, American mathematical society. Member of editorial boards of 9 journals.

Awards: Prize of Moscow mathematical society (1971). State Prize of Russian Federation in science and technique (1996) for the cycle of papers "Investigation of invariants of smooth manifolds and Hamiltonian dynamic systems". The Lomonosov Prize of Moscow State University for pedagogical activity (2001). Distinguished professor of Moscow State University from 2006.

In September 2001 the international conference "Topology, analysis and related topics" dedicated to the 60th birthday of A.S.Mishchenko held.

Supervisor of series Russian and international scientific projects . Took participation in the organization of series Russian and international conferences. Leader of Moscow scientific school on non commutative geometry and topology.

Area of scientific interest: geometry and topology and their applications.

Application to mathmetical modelling in ecology,molecular biology, bioinformatics.

Mathematical education, history of mathematica and mathematical education.

Basic results: study of algebraic and functional methods in the theory of smooth manifolds. He found neseccary and sufficient conditions of absence of elements of infinite filtration in K-theory, proved the Atiyah-Singer about K-groups of classifying spaces, found explicit formula for logarithm of universal formal group in the bordisms terms. He constructed algebraic signature invariants of non simply connected manifolds and the theory of Fredholm representations of discrete groups, proved homotopy invariance of higher signatures (Novikov conjecture) for large class of fundamental groups including discrete subgroups of non compact Lie groups.

He gave a method of integration of Hamiltonian system by non commutative algebra of first integrals, proved complete integrability of geodesic flows on symmetric spaces, found relation between quantization condition for the Maslov canonic operator and homological invariants of Lagrangian manifold. He found the solution of linear differential game of pursuit without discrimination of evasing object. He established an estimation of number of stationary solution of nonlinear stochastic equation modeling level regime of Caspian Sea. He built the theory of almost algebraic Poincare complexes and found local combinatorial Hirzebruch formula.

Educational activity:

Reading basic courses on linear algebra and geometry , classical differential geometry, differential geometry and topology, special courses on algebraic topology, vector bundles and K-theory, applied problem of geometry, variation problem in molecular biology. Carry out scientific seminars on geometry and topology and their applications. Supervisor of 19 Ph.D. and 4 doctoral dissertations

More than 150 scientific papers and books .

Invited addresses see here

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