Table of Contents

Volume 1: Integrable systems: a celebration of Emma Previator's 65th birthday 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 Knoerrer; 3. A note on the commutator of Hamiltonian vector fields Henryk Zoladek; 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 Dragovic, Milena Radnovic and Roger Fidele 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 Knoeppel, Franz Pedit and Ulrich Pinkall; 13. The Kowalewski top revisited F. Magri; 14. The Calogero-Francoise 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. Volume 2: 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 Sandor J. Kovacs; 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 Francoise 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 Cicero 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 Smajlovic; 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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A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

About the Author

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.