V. Buchstaber

Victor Buchstaber

Victor Buchstaber, famous mathematician, member of our Editorial board, is 60.

His first research work was in cobordism theory. He calculated the differential in the Atiyah—Hirzebruch spectral sequence in K-theory and complex cobordism theory, constructed Chern—Dold characters and the universal Todd genus in cobordisms, gave an alternative effective solution of the Milnor—Hirzebruch problem. His theory of double-valued formal groups lead to calculation of cobordism rings of complex manifolds having symplectic coverings and to the explicit construction of what are now called Buchstaber manifolds, generating these rings. His filtration in Hopf algebras and the Buchstaber spectral sequence were successfully applied to stable homotopy groups of spheres. Deformation theory for mappings to groups lead to the solution of the Novikov problem on multiplicative subgroups in operator doubles, and to construction of the quantum group of complex cobordisms. Later problems related both with algebraic geometry and integrable systems were added. Well-known is his work on sigma-functions on universal spaces of Jacobi varieties of algebraic curves that give effective solutions of important integrable systems. He created algebro-functional theory of symmetric powers of spaces and described algebraic varieties of polysymmetric polynomials.

We congratulate Victor on the occasion of his birthday and wish him success both in his own research, and in his vast activity for the benefit of the Russian and international mathematical community.

Yu. Ilyashenko, I. Krichever, S. Novikov, M. Tsfasman, V. Vassiliev

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