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Integrable Systems and Algebraic Geometry

Integrable Systems and Algebraic Geometry

Volume 1

Part of London Mathematical Society Lecture Note Series

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
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  • Publication planned for: April 2020
  • availability: Not yet published - available from April 2020
  • format: Paperback
  • isbn: 9781108715744

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About the Authors
  • 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. Each chapter gives a different perspective of the domain, from Franco Magri's exploration of Kowalewski's top from the viewpoint of bi-Hamiltonian geometry, to Horst Knörrer's discussion of the global symmetries of the three-dimensional Kepler problem.

    • 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
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    Product details

    • Publication planned for: April 2020
    • format: Paperback
    • isbn: 9781108715744
    • dimensions: 228 x 152 mm
    • contains: 50 b/w illus. 6 tables
    • availability: Not yet published - available from April 2020
  • Table of Contents

    Preface 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.

  • 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

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