Integrable Systems and Algebraic Geometry: Volume 2

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Ron Donagi (Edited by), Tony Shaska (Edited by)

9781108715775, Cambridge University Press

Paperback / softback, published 2 March 2020

536 pages, 4 b/w illus. 8 tables
22.8 x 15.2 x 2.8 cm, 0.76 kg

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.

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. ?-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 Smajlovi?
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.

Subject Areas: Algebraic geometry [PBMW], Differential calculus & equations [PBKJ]