Integrability, Quantization, and Geometry: I. Integrable Systems

ISBN-13: 9781470455910

Sergey Novikov;Igor Krichever;Oleg Ogievetsky

Opis

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. The 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's early interests.

Spis treści

• K. Aleshkin and K. Saito, Primitive forms without higher residue structure and integrable hierarchies (I)
• M. Alkadhem, G. Antoniou, and M, Feigin, Solutions of $BC_n$ type of WDVV equations
• P. P. Boalch, Topology of the Stokes phenomenon
• G. Cotti and A. Varchenko, Equivariant quantum differential equation and qKZ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and $\mathcyr$-theorem
• L. David and C. Hertling, Meromorphic connections over F-manifolds
• G. Jorjadze and S. Theisen, Canonical maps and integrability in $T\bar$ deformed 2d CFTs
• I. Krichever and A. Varchenko, Incarnations of XXX $\widehat{\mathfrak_N}$ Bethe ansatz equations and integrable hierarchies
• F. Magri, The Kowalewski separability conditions
• O. Mokhov and N. A. Strizhova, On the Liouville integrable reduction of the associativity equations in the case of three primary fields
• S. M. Natanzon and A. Yu. Orlov, Hurwitz numbers from matrix integrals over Guassian measure
• N. Reshetikhin, Spin Calogero-Moser models on symmetric spaces
• M. Semenov-Tian-Shansky, Quantum toda lattice: A challenge for representation theory
• A. O. Smirnov, M. V. Pavlov, V. B. Matveev, and V. S. Gerdjikov, Finite-gap solutions of the Mikhalev equation
• I. A. B. Strachan, Flat coordinates on orbit spaces: From Novikov algebras to cyclic quotient singularities
• K. Takasaki, Cubic Hodge integrals and integrable hierarchies of Volterra type
• G. Tian and G. Xu, Gauged Witten equation and adiabatic limit.