Integrable Systems and Algebraic Geometry
Integrable Systems and Algebraic Geometry
£79.99
GBPCreated 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.
- Brings together experts from the vast areas of research of integrable systems and algebraic geometry
- Contains a large collection of articles from different viewpoints and highlights the interconnections between different areas of mathematics
- Makes the theory accessible and will be a valuable source for graduate students and non-experts
Reviews & endorsements
'I compliment the authors for the fact that the articles are all well-written and very interesting. However, the consistent high-quality throughout the collection suggests that the editors and the researcher to whom it is dedicated also deserve to share some of the credit. This two volume set captures a fascinating snapshot of the current state of this (literally) dynamic area of algebraic geometry research. It is highly recommended as a reference and an inspiration for anyone interested in this subject.' Alex Kasman, MAA Reviews
'This is a book that will mainly be of interest to people who are at least aware of Emma Prevatio. It gives a good indication of the many areas of mathematics influenced by her work. It is clearly aimed more at working mathematicians or post-graduate students.' John Bartlett, Institute of Mathematics and its Applications
Product details
April 2020Paperback
9781108715744
420 pages
228 × 152 × 22 mm
0.61kg
50 b/w illus. 6 tables
Available
Table of Contents
- Integrable systems: a celebration of Emma Previator's 65th birthday Ron Donagi and Tony Shaska
- 1. Trace ideal properties of a class of integral operators Fritz Gesztesy and Roger Nichols
- 2. Explicit symmetries of the Kepler Hamiltonian Horst Knörrer
- 3. A note on the commutator of Hamiltonian vector fields Henryk Żołądek
- 4. Nodal curves and a class of solutions of the Lax equation for shock clustering and Burgers turbulence Luen-Chau Li
- 5. Solvable dynamical systems in the plane with polynomial interactions Francesco Calogero and Farrin Payandeh
- 6. The projection method in classical mechanics A. M. Perelomov
- 7. Pencils of quadrics, billiard double-reflection and confocal incircular nets Vladimir Dragović, Milena Radnović and Roger Fidèle Ranomenjanahary
- 8. Bi-flat F-manifolds: a survey Alessandro Arsie and Paolo Lorenzoni
- 9. The periodic 6-particle Kac–Van Moerbeke system Pol Vanhaecke
- 10. Integrable mappings from a unified perspective Tova Brown and Nicholas M. Ercolani
- 11. On an Arnold–Liouville type theorem for the focusing NLS and the focusing mKdV equations T. Kappeler and P. Topalov
- 12. Commuting Hamiltonian flows of curves in real space forms Albert Chern, Felix Knöppel, Franz Pedit and Ulrich Pinkall
- 13. The Kowalewski top revisited F. Magri
- 14. The Calogero–Françoise integrable system: algebraic geometry, Higgs fields, and the inverse problem Steven Rayan, Thomas Stanley and Jacek Szmigielski
- 15. Tropical Markov dynamics and Cayley cubic K. Spalding and A. P. Veselov
- 16. Positive one-point commuting difference operators Gulnara S. Mauleshova and Andrey E. Mironov.
