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El. knyga: Integrable Systems and Algebraic Geometry: Volume 2

Edited by (University of Pennsylvania), Edited by (Oakland University, Michigan)
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Created as a celebration of mathematical pioneer Emma Previato, this comprehensive second volume highlights the connections between her main fields of research, namely algebraic geometry and integrable systems. Written by leaders in the field, the text is accessible to graduate students and non-experts, as well as researchers.

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.

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A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
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 Sįndor J. Kovįcs;
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 DubrovinFrobenius manifolds to geometry of moduli spaces Dmitry
Korotkin;
8. The rigid body dynamics in an ideal fluid: Clebsch top and
Kummer surfaces Jean-Pierre Franēoise and Daisuke Tarama;
9. An extension of
Delsarte, Goethals and Mac Williams theorem on minimal weight codewords to a
class of ReedMuller type codes Cķcero 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.
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 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.
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