Serguei Novikov

Novikov was born March 20, 1938 in Gorki, into a family of outstanding mathematicians. His father, Petr Sergeevich Novikov (1901-1975), was an academician, an outstanding expert in mathematical logic, algebra, set theory, and function theory; his mother, Lyudmila Vsevolodovna Keldysh (1904-1976), was a professor, a well-known expert in geometric topology and set theory. Novikov received his mathematical education in the Faculty of Mathematics and Mechanics of Moscow University (1955-1960), and he has worked there since 1964 in the Department of Differential Geometry; since 1983 he has been head of the Department of Higher Geometry and Topology of Moscow University (see S.P.Novikov Seminar). Beginning in 1992 he regularly worked at the University of Maryland at College Park as a Visiting Professor. In September 1996 he became a full-time professor at the University of Maryland at College Park in the Department of Mathematics and the Institute for Physical Science and Technology.

In 1960 Novikov enrolled as a research student at the Steklov Institute of Mathematics, where his supervisor was M. M. Postnikov; since 1963 he has been on the staff there. He was awarded the degree of Ph.D. there in 1964, and that of Doctor of Science in 1965. In 1966 he was elected Corresponding Member of the Academy of Sciences of the USSR, and in 1981 a full member. Since 1984 he has been head of the Department of Geometry and Topology of the Mathematical Institute of the Academy of Sciences, and in charge of the problem committee of Geometriya i topologiya (Geometry and Topology) at the Mathematics Division of the Academy of Sciences of the USSR. He has been head of the Mathematics Division at the L. D. Landau Institute for Theoretical Physics of the Academy of Sciences since 1971, where he works closely with the physicists. During the period 1985-1996 Novikov served as Persident of the Moscow Mathematical Society, and during 1986-1990 he was also a Vice-President of the International Association in Mathematical Physics.

Since 1971 his scientific work has played an important part in building a "bridge" between modern mathematics and theoretical physics. Some of Novikov's papers can be divided as follows:

Papers before 1971

Papers after 1971

Novikov's main area of current scientific interests: Geometry, Topology and Mathematical Physics.

Awards and Honors

Students of Sergei Novikov

More than 30 of Novikov's students have been awarded the Candidate Degree (equivalent to Ph.D.), and of these V. M. Buchstaber, A. S. Mishchenko, O. I. Bogoyavlenskii, I. M. Krichever, B. A. Dubrovin, G. G. Kasparov, F. A. Bogomolov, S. P.Tsarev, I. A.Taimanov, A. P.Veselov M. A. Brodskii, V. V. Vedenyapin, R. Nadiradze, V. L . Golo, S. M. Gusein-Zade have been awarded the degree of Doctor of Science (Scientific Degree, equivalent to the level of full professor in former USSR and in Russia).

In addition to those mentioned above, other Novikov pupils with the Candidate Degree (corre-spondent to Ph.D. level in the West) include I. A. Volodin, N. V. Panov, A. L. Brakhman, P. G. Grinevich, O. I. Mokhov, A. V. Zorich, F. A. Voronov, G. S. D. Grigoryan, A. S. Lyskova, E. Potemin, M. Pavlov, L. Alania, D. Millionshikov, V. Peresetski, I. Dynnikov, A. Maltsev, V. Sadov, Le Tu Thang, S. Piunikhin, A. Lazarev.
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List of Novikov's papers

1. Cohomology of the Steenrod algebra, Dokl. Akad. Nauk SSSR 128 (1959) 893-895.

2. Some problems in the topology of manifolds connected with the theory of Thom spaces, Dokl. Akad. Nauk SSSR 132 (1960) 1031-1034. = Soviet Math. Dokl. 1 (1960) 717-719.

3. On embedding simply-connected manifolds in Euclidean space, Dokl. Akad. Nauk SSSR 138 (1961) 775-778. = Soviet Math. Dokl. 2 (1961) 718-721.

4. Smooth manifolds of general homotopy type, Internat. Cong. Math., Stockholm 1962, section 4, 139.

5. On the diffeomorphism of simply-connected manifolds, Dokl. Akad. Nauk SSSR 143 (1962) 1046-1049. = Soviet Math. Dokl. 3 (1962) 540-543.

6. Homotopy properties of Thom complexes, Mat. Sb. 57 (1962) 407-422.

7. Homotopy properties of the group of diffeomorphisms of the sphere, Dokl. Akad. Nauk SSSR 148 (1963) 32-35. = Soviet Math. Dokl. 4 (1963) 32-35.

97. Analytical homotopy theory. Rigidity of homotopic integrals, Dokl. Akad. Nauk SSSR, 1985, v. 283, N 5, 1088-1091.

98. Integrable systems, I. Current problem in mathematics. Fundamental directions. VINITI, 1985, v. 4, 179-284 (with B. A. Dubrovin and I. M. Krichever).

99. Two-diinensioirlal periodic Schrödinger operators and Prym's theta-fiinctions, in Geometry Today, Internat. Conf. Rome, June 1984, Boston, 1985, 106-118 (with A. P.Veselov and I. M. Krichever).

100. Differential geometly and the averaging method for field-theoretic systems, Proc. III Internat. Symp. on Selected Problem in Statistical Mechanics (Dubna, 1984), Joint. Institute of Nuclear Research, Dubna, 1985, vol. 2, 106-118.

101. Modern geometry. Methods and applications, 2nd revised edition, Nauka, Moscow 1986 (with B. A. Dubrovin and A. T. Fomenko).

102. Bloch homology. Critical points of functions and closed I-forms, Dokl. Akad. Nauk SSSR, 1986, v. 287, N 6, 1321-1324.

103. Morse inequalities and von Neumann factors, Dokl. Akad. Nauk SSSR, 1986, v. 289, N 2, 289-292.

104. Topology I. Current problem in mathematics. Fundamental directions, VINITI, 1986, v. 12, 5-251.

105. Two-dimensional Schrödinger operators: Inverse scattering transform and evolutional equations, Phys. D18, 1986, 267-273 (with A. P. Veselov).

106. Vladimir Abramovich Rokhiin (obituary), Uspekhi Mat, Nauk, 1986, v. 41, N 3, 159-163 (with V. I. Arnol'd, D. B. Fuks, A. N. Kolmogorov, Ya. G. Sinai, A. M. Vershik, and 0. Ya. Viro).

107. Evolution of the Whitham zone in the Korteweg-de Vries theory, Dokl. Akad. Nauk SSSR, 1987, v. 294, N 2, 325-229 (with V. V. Avilov).

108. Elements of differential geometry and topology, Nauk, Moscow, 1987 (with A. T. Fomenko).

109, Evolution of the Whitham zone in the Korteweg-de Vries theory, Dokl. Akad. Nauk SSSR, 1987, v. 295, N 2, 345-349 (with V. V. Avilov and I. M. Krichever).

110. Algebras of Virasoro type, Riemann surfaces and structures in the theory of solitons, Funktsional. Anal. i Prilozhen., 1987, v. 21, N 2, 46-63 (with I. M. Krichever).

111. Algebras of Virasoro type, Riemann surfaces, and strings in Minkowski space, Funktsional. Anal. i Prilozhen., 1937, v. 21, N 4, 47-61 (with I. M. Krichever).

112. Two-dimensiottal Schrödinger operator and solitons 3 -dimensional integrable systems VIII Internat. Congr. on Math. Physics, Marseille 1986, Wered Scientific Publ. 1987, 226-241.

Papers of the 1988-1997 period

113. The two-dimensional "inverse scattering problem" for negative energy and generalized analytic functions, I. Energy below the basis state, Funktsional. Anal. i Prilozhen., 1988, v. 22, N 1, 23-33 (with P. P. Grinevich).

114. Analytical theory of homotopy groups, in Topology and Geometry, Rochlin Seminar, Lecture Notes in Math., 1988, vol. 1346, 99-112, Springer-Verlag.

115. Virasoro-type algebras, pseudo-tensor of energy-momentum and operator expansions on the Riemann surfaces, Funktsional. Anal. i Prilozhen. 1989, v. 23, N 1 (with I. M. Krichever).

116. Riemanti surfaces, operator fields, strings. Analogues of the Fourier-Laurent bases, in Memorial Volume for Vadim Knizhnik, "Physics and Mathematics of Strings", eds. L. Brink, D. Friedan, A. M. Polyakov, World Scientific, Singapore, 1989, 356-388 (with I. M. Krichever).

117. Hydrodynamics of the soliton lattices. Differential geometry and Hamiltonian formalism. Uspekhi Mat. Nauk, 1989, v. 44, N 6, 29-98 (with B. A. Dubrovin).

118. Qn the quantization of finite-zoned potentials in connection with string theory, Funktsional. Anal. i Prilozhen., 1990. v 24, N 4.

119. On the equation [L,A] = e.1, RIMS publications, 1991 (Transactions of the Kyoto workshop in the string theory. May 5-21, 1990).

120. Hydrodynamics of the soliton lattices and differential geometry. (Collection of the survey articles. Potsdam. 1992, edited by A. Fokas.)

121. Quasiperiodic structures in topology, in the Proceeding of the Conference: Topological Methods in Modern Mathematics", June 15-22, 1991, dedicated to the 60-th birthday of T. Milnor. Stonybrook University, 1993.

122. Different doubles of the Hopf algebras. Operator algebras on the quantum groups and complex cobordisms, Uspekhi Math. Mauk, 1992, v. 47 iss. 5, pp. 189-190.

123. Integrability in mathematics and theoretical physics: Solitons. The Mathematical Intelligencer, 1992, Vol. 14, N 4. Springer-Veriag, New York.

124. On the Liouville form of the Poisson bracket of hydrodynamic type and nonlinear WKB. Uspechi Math. Nauk, 1993, v. 48, iss. 1 (with A. Maltzev.)

125. Solitons and geometry. Fermi lectures 1992. Scuola Norm. Sup. di Pisa, Cambridge University Press, 1994.

126. String Equation -2. Physical Solution, Algebra and Analysis, 1994, v. 6 iss. 3, pp. 118-140 (with P. G. Grinevich).

127. The semiclassical electron in a magnetic field and lattice. Some problems of the Low Dimensional "Periodic" Topology, Geometric and Functional Analysis, 1995, v. 5, N 2.

128. Topology- 1. Enclyclopedia of Mathematical Sciences, v. 12, Springer Verlag, 1995.

129. Nonselfinersecting magnetic orbits on the plane. Proof of Principle of the Overthrowing of the Cycles, Topics in Topology and Mathematical Physics, 1995, AMS Translations (2), v. 170 (with P. G. Orinevich).

130. Exactly solvable periodic 2-D Schrödinger operators, Russia Math. Surveys, 1995, N 6 (in Russiah) (with A. P. Veselov).

131. Topological quantum numbers observable in the conductivity of normal metals, 1996, Letters of JETF, v. 63, iss. 10, pp. 809-813 (in Russian) (with A. Maltzev).

132. Laplace transformations and exactly solvable 2-dimensional Schrödinger operators, 1997, AMS Translations, ser. 2, v. 179, pp. 109-132 (with A. P. Veselov).

133. Algebraic properties of 2D discrete Schrödinger operators, Russia Math. Surveys, 1997, v. 32, N 1, pp. 223-224 (in Russian).

134. Discrete spectral symmetries of low dimensional differential and difference Schrödinger operators on the Euclidean lattices and 2-manifolds, Russia Math Surveys, 1997, v. 32 N 5 (in Russian) (with I. A. Dynnikov).