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Integrable Systems and Algebraic Geometry

Integrable Systems and Algebraic Geometry

Volume 2

c.$99.00 ( )

Part of London Mathematical Society Lecture Note Series

Ron Donagi, Tony Shaska, Alexandru Buium, Boris Dubrovin, Sándor J. Kovács, Yuri G. Zarhin, Adrian Clingher, Andreas Malmendier, V. M. Buchstaber, V. Z. Enolski, D. V. Leykin, Dmitry Korotkin, Jean-Pierre Françoise, Daisuke Tarama, Cícero Carvalho, Victor G. L. Neumann, L. M. Bates, R. C. Churchill, Roland Schmidt, Jiyro Komeda, Shigeki Matsutani, James Cogdell, Jay Jorgenson, Lejla Smajlović, Mauro Spera, Ivan Horozov, Vladimir Retakh, Vladimir Rubtsov, Georgy Sharygin
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  • Publication planned for: April 2020
  • availability: Not yet published - available from April 2020
  • format: Paperback
  • isbn: 9781108715775

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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. The articles in this second volume discuss areas related to algebraic geometry, one of the central areas of mathematics, and cover a wide scope of topics, including the Bergman tau-function and Jacobi inversion formulae.

    • 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: 9781108715775
    • dimensions: 228 x 152 mm
    • contains: 4 b/w illus. 8 tables
    • availability: Not yet published - available from April 2020
  • Table of Contents

    Preface Ron Donagi and Tony Shaska
    1. Arithmetic analogues of Hamiltonian systems Alexandru Buium
    2. Algebraic spectral curves over Q and their tau-functions Boris Dubrovin
    3. Frobenius split anticanonical divisors Sándor J. Kovács
    4. Halves of points of an odd degree hyperelliptic curve in its jacobian Yuri G. Zarhin
    5. Normal forms for Kummer surfaces Adrian Clingher and Andreas Malmendier
    6. σ-functions: old and new results V. M. Buchstaber, V. Z. Enolski and D. V. Leykin
    7. Bergman tau-function: from Einstein equations and Dubrovin–Frobenius manifolds to geometry of moduli spaces Dmitry Korotkin
    8. The rigid body dynamics in an ideal fluid: Clebsch top and Kummer surfaces Jean-Pierre Françoise and Daisuke Tarama
    9. An extension of Delsarte, Goethals and MacWilliams theorem on minimal weight codewords to a class of Reed–Muller type codes Cícero Carvalho and Victor G. L. Neumann
    10. A primer on Lax pairs L. M. Bates and R. C. Churchill
    11. Lattice-theoretic characterizations of classes of groups Roland Schmidt
    12. Jacobi inversion formulae for a curve in Weierstrass normal form Jiyro Komeda and Shigeki Matsutani
    13. Spectral construction of non-holomorphic Eisenstein-type series and their Kronecker limit formula James Cogdell, Jay Jorgenson and Lejla Smajlović
    14. Some topological applications of theta functions Mauro Spera
    15. Multiple Dedekind zeta values are periods of mixed Tate motives Ivan Horozov
    16. Noncommutative cross-ratio and Schwarz derivative Vladimir Retakh, Vladimir Rubtsov and Georgy Sharygin.

  • 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, Alexandru Buium, Boris Dubrovin, Sándor J. Kovács, Yuri G. Zarhin, Adrian Clingher, Andreas Malmendier, V. M. Buchstaber, V. Z. Enolski, D. V. Leykin, Dmitry Korotkin, Jean-Pierre Françoise, Daisuke Tarama, Cícero Carvalho, Victor G. L. Neumann, L. M. Bates, R. C. Churchill, Roland Schmidt, Jiyro Komeda, Shigeki Matsutani, James Cogdell, Jay Jorgenson, Lejla Smajlović, Mauro Spera, Ivan Horozov, Vladimir Retakh, Vladimir Rubtsov, Georgy Sharygin

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