Integrable systems and algebraic geometry : a celebration of Emma Previato's 65th birthday

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Integrable systems and algebraic geometry : a celebration of Emma Previato's 65th birthday

edited by Ron Donagi, Tony Shaska

（London Mathematical Society lecture note series, 458-459）

Cambridge University Press, 2020

  • : 2 v. set : pbk
  • v. 1 : pbk
  • v. 2 : pbk

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Includes bibliographical references

Description and Table of Contents

Volume

v. 1 : pbk ISBN 9781108715744

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. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.

Table of Contents

  • 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

v. 2 : pbk ISBN 9781108715775

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.

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 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.
Volume

: 2 v. set : pbk ISBN 9781108785495

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 work is split into two volumes, with the first covering a wide range of areas related to integrable systems, and the second focusing on algebraic geometry and its applications.

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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