Integrable Systems and Algebraic Geometry: Volume 1

Ron Donagi, Tony Shaska

• Publisher: Cambridge University Press
• Year: 2020
• ISBN:
  9781108802062
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.

Table of contents

• Cover
• Series information
• Title page
• Copyright information
• Contents of Volume 1
• Contents of Volume 2
• Integrable Systems: A Celebration of Emma Previato's 65th Birthday
• 1 Trace Ideal Properties of a Class of Integral Operators
• 2 Explicit Symmetries of the Kepler Hamiltonian
• 3 A Note on the Commutator of Hamiltonian Vector Fields
• 4 Nodal Curves and a Class of Solutions of the Lax Equation for Shock Clustering and Burgers Turbulence
• 5 Solvable Dynamical Systems in the Plane with Polynomial Interactions
• 6 The Projection Method in Classical Mechanics
• 7 Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets
• 8 Bi-Flat F-Manifolds: A Survey
• 9 The Periodic 6-Particle Kac-van Moerbeke System
• 10 Integrable Mappings from a Unified Perspective
• 11 On an Arnold-Liouville Type Theorem for the Focusing NLS and the Focusing mKdV Equations
• 12 Commuting Hamiltonian Flows of Curves in Real Space Forms
• 13 The Kowalewski Top Revisited
• 14 The Calogero-Françoise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem
• 15 Tropical Markov Dynamics and Cayley Cubic
• 16 Positive One–Point Commuting Difference Operators