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. 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.

Readership

Graduate students and research mathematicians interested in mathematical physics, geometry, and topology.

Table of Contents

• S. P. Novikov -- The second half of the 20th century and its conclusion: Crisis in the physics and mathematics community in Russia and in the West
• V. M. Buchstaber -- Interview with Sergey P. Novikov
• V. M. Buchstaber and S. Yu. Shorina -- The \(w\)-function of the KdV hierarchy
• A. Campillo, F. Delgado, and S. M. Gusein-Zade -- On the zeta functions of a meromorphic germ in two variables
• B. Dubrovin -- On almost duality for Frobenius manifolds
• I. A. Dynnikov -- Finitely presented semigroups in knot theory. Oriented case
• M. Farber and S. Yuzvinsky -- Topological robotics: Subspace arrangements and collision free motion planning
• P. G. Grinevich and P. M. Santini -- The initial-boundary value problem on the interval for the nonlinear Schrödinger equation. The algebro-geometric approach. I
• H. M. Khudaverdian and T. Voronov -- On odd Laplace operators. II
• Yu. Klimov, A. Korzh, and S. Natanzon -- From 2D Toda hierarchy to conformal maps for domains of the Riemann sphere
• I. Krichever -- Integrable chains on algebraic curves
• S. B. Kuksin -- Fifteen years of KAM for PDE
• D. V. Millionschikov -- Graded filiform Lie algebras and symplectic nilmanifolds
• A. G. Sergeev -- Adiabatic limit in the Seiberg-Witten equations
• O. K. Sheinman -- Affine Krichever-Novikov algebras, their representations and applications
• I. A. Taimanov -- Tame integrals of motion and o-minimal structures