Integrable Systems and Algebraic Geometry

Volume 1

£79.99

Part of London Mathematical Society Lecture Note Series

Editors:
Ron Donagi, University of Pennsylvania
Tony Shaska, Oakland University, Michigan

Ron Donagi, Tony Shaska, Fritz Gesztesy, Roger Nichols, Horst Knörrer, Henryk Żołądek, Luen-Chau Li, Francesco Calogero, Farrin Payandeh, A. M. Perelomov, Vladimir Dragović, Milena Radnović, Roger Fidèle Ranomenjanahary, Alessandro Arsie, Paolo Lorenzoni, Pol Vanhaecke, Tova Brown, Nicholas M. Ercolani, T. Kappeler, P. Topalov, Albert Chern, Felix Knöppel, Franz Pedit, Ulrich Pinkall, F. Magri, Steven Rayan, Thomas Stanley, Jacek Szmigielski, K. Spalding, A. P. Veselov, Gulnara S. Mauleshova, Andrey E. Mironov

View all contributors

Date Published: April 2020
availability: Available
format: Paperback
isbn: 9781108715744

Rate & review

£ 79.99
Paperback

Add to cart Add to wishlist

Other available formats:
eBook

Looking for an inspection copy?

This title is not currently available on inspection

Description

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.
- 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
Read more
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
See more reviews
Customer reviews

Not yet reviewed
Be the first to review

Log in to review

Review was not posted due to profanity
×

, create a review

(If you're not , sign out)

Please enter the right captcha value

Please enter a star rating.

Your review must be a minimum of 12 words.

How do you rate this item?

Reviews must contain at least 12 words about the product.

×

Product details
- Date Published: April 2020
- format: Paperback
- isbn: 9781108715744
- length: 420 pages
- dimensions: 228 x 152 x 22 mm
- weight: 0.61kg
- contains: 50 b/w illus. 6 tables
- availability: 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.
Look Inside
Editors
Ron Donagi, University of Pennsylvania
Ron Donagi is Professor of Mathematics and Physics at the University of Pennsylvania. He works in algebraic geometry and string theory, and is a Fellow of the American Mathematical Society. He has written and edited several books, including Integrable Systems and Quantum Groups (2009).
Tony Shaska, Oakland University, Michigan
Tony Shaska is Associate Professor in the Department of Mathematics at Oakland University, Michigan. He works in algebraic and arithmetic geometry with an emphasis on algebraic curves and their Jacobians, including arithmetic aspects. He is an active researcher and has edited many books including Computational Aspects of Algebraic Curves (2005), Advances in Coding Theory and Cryptography (2007), Advances on Superelliptic Curves and Their Applications (2015) and Algebraic Curves and Their Applications (2019). He has been Editor in Chief of the Albanian Journal of Mathematics since 2007.
Contributors
Ron Donagi, Tony Shaska, Fritz Gesztesy, Roger Nichols, Horst Knörrer, Henryk Żołądek, Luen-Chau Li, Francesco Calogero, Farrin Payandeh, A. M. Perelomov, Vladimir Dragović, Milena Radnović, Roger Fidèle Ranomenjanahary, Alessandro Arsie, Paolo Lorenzoni, Pol Vanhaecke, Tova Brown, Nicholas M. Ercolani, T. Kappeler, P. Topalov, Albert Chern, Felix Knöppel, Franz Pedit, Ulrich Pinkall, F. Magri, Steven Rayan, Thomas Stanley, Jacek Szmigielski, K. Spalding, A. P. Veselov, Gulnara S. Mauleshova, Andrey E. Mironov