Softcover ISBN:  9781470455910 
Product Code:  PSPUM/103.1 
516 pp 
List Price:  $137.00 
MAA Member Price:  $123.30 
AMS Member Price:  $109.60 
Electronic ISBN:  9781470464349 
Product Code:  PSPUM/103.1.E 
516 pp 
List Price:  $137.00 
MAA Member Price:  $123.30 
AMS Member Price:  $109.60 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 103; 2021MSC: Primary 14; 33; 53;
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.ReadershipGraduate students and researchers interested in mathematical physics, enumerative and differential geometry, and geometric representation theory.
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Table of Contents

Articles

Konstantin Aleshkin and Kyoji Saito  Primitive Forms without Higher Residue Structure and Integrable Hierarchies (I)

Maali Alkadhem, Georgios Antoniou and Misha Feigin  Solutions of $BC_{n}$ Type of WDVV Equations

P. P. Boalch  Topology of the Stokes phenomenon

Giordano Cotti and Alexander Varchenko  Equivariant quantum differential equation and qKZ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and \textcyr{B}Theorem

Liana David and Claus Hertling  Meromorphic Connections over Fmanifolds

George Jorjadze and Stefan Theisen  Canonical maps and integrability in $T\bar T$ deformed 2d CFTs

Igor Krichever and Alexander Varchenko  Incarnations of XXX $\widehat {\frak {sl}_N}$ Bethe ansatz equations and integrable hierarchies

Franco Magri  The Kowalewski separability conditions

O.I. Mokhov and N.A. Strizhova  On the Liouville Integrable Reduction of the Associativity Equations in the Case of Three Primary Fields

Sergey M. Natanzon and Aleksandr Yu. Orlov  Hurwitz numbers from matrix integrals over Gaussian measure

Nicolai Reshetikhin  Spin CalogeroMoser models on symmetric spaces

Michael SemenovTianShansky  Quantum Toda Lattice: a Challenge for Representation Theory

A. O. Smirnov, M. V. Pavlov, V. B. Matveev and V. S. Gerdjikov  FiniteGap Solutions of the Mikhalëv Equation

Ian A.B. Strachan  Flat coordinates on orbit spaces: from Novikov algebras to cyclic quotient singularities

Kanehisa Takasaki  Cubic Hodge integrals and integrable hierarchies of Volterra type

Gang Tian and Guangbo Xu  Gauged Witten Equation and Adiabatic Limit


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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.
Graduate students and researchers interested in mathematical physics, enumerative and differential geometry, and geometric representation theory.

Articles

Konstantin Aleshkin and Kyoji Saito  Primitive Forms without Higher Residue Structure and Integrable Hierarchies (I)

Maali Alkadhem, Georgios Antoniou and Misha Feigin  Solutions of $BC_{n}$ Type of WDVV Equations

P. P. Boalch  Topology of the Stokes phenomenon

Giordano Cotti and Alexander Varchenko  Equivariant quantum differential equation and qKZ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and \textcyr{B}Theorem

Liana David and Claus Hertling  Meromorphic Connections over Fmanifolds

George Jorjadze and Stefan Theisen  Canonical maps and integrability in $T\bar T$ deformed 2d CFTs

Igor Krichever and Alexander Varchenko  Incarnations of XXX $\widehat {\frak {sl}_N}$ Bethe ansatz equations and integrable hierarchies

Franco Magri  The Kowalewski separability conditions

O.I. Mokhov and N.A. Strizhova  On the Liouville Integrable Reduction of the Associativity Equations in the Case of Three Primary Fields

Sergey M. Natanzon and Aleksandr Yu. Orlov  Hurwitz numbers from matrix integrals over Gaussian measure

Nicolai Reshetikhin  Spin CalogeroMoser models on symmetric spaces

Michael SemenovTianShansky  Quantum Toda Lattice: a Challenge for Representation Theory

A. O. Smirnov, M. V. Pavlov, V. B. Matveev and V. S. Gerdjikov  FiniteGap Solutions of the Mikhalëv Equation

Ian A.B. Strachan  Flat coordinates on orbit spaces: from Novikov algebras to cyclic quotient singularities

Kanehisa Takasaki  Cubic Hodge integrals and integrable hierarchies of Volterra type

Gang Tian and Guangbo Xu  Gauged Witten Equation and Adiabatic Limit