Integrable Systems and Algebraic Geometry

Volume 2

£92.99

Part of London Mathematical Society Lecture Note Series

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

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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Date Published: April 2020
availability: Available
format: Paperback
isbn: 9781108715775

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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. 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.
- 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
- Date Published: April 2020
- format: Paperback
- isbn: 9781108715775
- length: 536 pages
- dimensions: 228 x 152 x 28 mm
- weight: 0.76kg
- contains: 4 b/w illus. 8 tables
- availability: Available
Table of Contents
Algebraic geometry: a celebration of Emma Previato's 65th birthday 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 Mac Williams 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.
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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