Integrability, Quantization, and Geometry

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.\n\nThe contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin\x27s early interests.

Edited by Sergey Novikov: University of Maryland, College Park, MD and Steklov Institute of Mathematics, Moscow, Russia, Igor Krichever: Columbia University, New York, NY and Skoltech, Moscow, Russia, Oleg Ogievetsky: Center of Theoretical Physics, Marseille, France and Labadev Physical Institute, Moscow, Russia, Senya Shlosman: Center of Theoretical Physics, Marseille, France and Skoltech, Moscow, Russia