This volume contains a selection of papers based on presentations given at the S. P. Novikov seminar held at the Steklov Mathematical Institute in Moscow. The topics and speakers were chosen by the well-known expert, S. P. Novikov, one of the leading mathematicians of the twentieth century. His diverse interests are the tradition of the seminar and are reflected in the topics presented in the book. The book begins with Novikov's paper analyzing the position of mathematics and theoretical physics at the beginning of the new millennium. Following is an interview with Novikov published in the ""Newsletter of the European Mathematical Society"" presenting the genesis of many of his ideas and his scientific school. The remaining articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
The second half of the 20th century and its conclusion: Crisis in the physics and mathematics community in Russia and in the West by S. P. Novikov Interview with Sergey P. Novikov by V. M. Buchstaber The $w$-function of the KdV hierarchy by V. M. Buchstaber and S. Yu. Shorina On the zeta functions of a meromorphic germ in two variables by A. Campillo, F. Delgado, and S. M. Gusein-Zade On almost duality for Frobenius manifolds by B. Dubrovin Finitely presented semigroups in knot theory. Oriented case by I. A. Dynnikov Topological robotics: Subspace arrangements and collision free motion planning by M. Farber and S. Yuzvinsky The initial-boundary value problem on the interval for the nonlinear Schrodinger equation. The algebro-geometric approach. I by P. G. Grinevich and P. M. Santini On odd Laplace operators. II by H. M. Khudaverdian and T. Voronov From 2D Toda hierarchy to conformal maps for domains of the Riemann sphere by Yu. Klimov, A. Korzh, and S. Natanzon Integrable chains on algebraic curves by I. Krichever Fifteen years of KAM for PDE by S. B. Kuksin Graded filiform Lie algebras and symplectic nilmanifolds by D. V. Millionschikov Adiabatic limit in the Seiberg-Witten equations by A. G. Sergeev Affine Krichever-Novikov algebras, their representations and applications by O. K. Sheinman Tame integrals of motion and o-minimal structures by I. A. Taimanov.