Integrable Systems and Algebraic Geometry: Volume 2

Ron Donagi, Tony Shaska

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN:
  9781108715775
• eBook ISBN:
  9781108807920
• Topic: Mathematics
• Subtopic: Topology
• 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. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.

Table of contents

• Cover
• Series information
• Title page
• Copyright information
• Contents of Volume 2
• Contents of Volume 1
• Algebraic Geometry: A Celebration of Emma Previato's 65th Birthday
• 1 Arithmetic Analogues of Hamiltonian Systems
• 2 Algebraic Spectral Curves over Q and their Tau-Functions
• 3 Frobenius Split Anticanonical Divisors
• 4 Halves of Points of an Odd Degree Hyperelliptic Curvein its Jacobian
• 5 Normal Forms for Kummer Surfaces
• 6 σ-Functions: Old and New Results
• 7 Bergman Tau-Function: From Einstein Equations and Dubrovin-Frobenius Manifolds to Geometry of Moduli Spaces
• 8 The Rigid Body Dynamics in an Ideal Fluid: Clebsch Top and Kummer Surfaces
• 9 An Extension of Delsarte, Goethals and Mac Williams Theorem on Minimal Weight Codewords to a Class of Reed-Muller Type Codes
• 10 A Primer on Lax Pairs
• 11 Lattice-Theoretic Characterizations of Classes of Groups
• 12 Jacobi Inversion Formulae for a Curve in Weierstrass Normal Form
• 13 Spectral Construction of Non-Holomorphic Eisenstein-Type Series and their Kronecker Limit Formula
• 14 Some Topological Applications of Theta Functions
• 15 Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives
• 16 Noncommutative Cross-Ratio and Schwarz Derivative