Integrable Systems and Algebraic Geometry: Volume 1

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.

• 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 Knörrer; 3. A note on the commutator of Hamiltonian vector fields Henryk Żołądek; 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 Dragović, Milena Radnović and Roger Fidèle 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 Knöppel, Franz Pedit and Ulrich Pinkall; 13. The Kowalewski top revisited F. Magri; 14. The Calogero–Françoise 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.

'I compliment the authors for the fact that the articles are all well-written and very interesting. However, the consistent high-quality throughout the collection suggests that the editors and the researcher to whom it is dedicated also deserve to share some of the credit. This two volume set captures a fascinating snapshot of the current state of this (literally) dynamic area of algebraic geometry research. It is highly recommended as a reference and an inspiration for anyone interested in this subject.' Alex Kasman, MAA Reviews