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Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
V. M. Buchstaber, Steklov Institute of Mathematics, Moscow, Russia.B. A. Dubrovin, SISSA, Trieste, Italy.I. M. Krichever, Columbia University, New York, NY, USA.
Algebras of conjugacy classes of partial elements by A. V. Alexeevski and S. M. NatanzonHarmonic spheres in the Hilbert-Schmidt Grassmannian by I. Beloshapka and A. SergeevOn uniformly rational varieties by F. Bogomolov and C. BohningIST of KPII equation for perturbed multisoliton solutions by M. Boiti, F. Pempinelli, and A. K. PogrebkovHopf algebras and homology of loop suspension spaces by V. Buchstaber and J. GrbicQuantum ordering for quantum geodesic functions of orbifold Riemann surfaces by L. O. Chekhov and M. MazzoccoPencils of conics and biquadratics, and integrability by V. DragovicGromov-Witten invariants and integrable hierarchies of topological type by B. DubrovinOn typical leaves of a measured foliated 2-complex of thin type by I. Dynnikov and A. SkripchenkoVolume of a simplex as a multivalued algebraic function of the areas of its two-faces by A. A. GaifullinDiscrete analogues of Dirac's magnetic monopole and binary polyhedral groups by G. M. Kemp and A. P. VeselovGeometric constructions on the algebra of densities by H. M. Khudaverdian and Th. Th. VoronovAmoebas, Ronkin function and Monge-Ampere measures of algebraic curves with marked points by I. KricheverThe averaging of multi-dimensional Poisson brackets for systems having pseudo-phases by A. Ya. MaltsevPeriodic and rapid decay rank two self-adjoint commuting differential operators by A. E. MironovCommuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients by O. I. MokhovClassical mechanical systems with one-and-a-half degrees of freedom and Vlasov kinetic equation by M. V. Pavlov and S. P. TsarevLax operator algebras of type G2 by O. K. Sheinman