November 29, 2023

Thematic Program in Partial Differential Equations

Workshop on Integrable and Near-integrable Hamiltonian PDE
(joint with le Centre de recherches mathématiques)
to be held at The Fields Institutue
May 17-21, 2004

Organizing Committee:
W. Craig (Chair), P. Deift, S. Kuksin, P. Olver, J. Toth, P. Winternitz

The theory of integrable partial differential equations (PDEs) has classical origins in the 19th c., and several examples already appear in the book of Ince. However its modern inception and the realization of the close analogy with Hamiltonian mechanics dates to the 1960's. Starting with the KdV equation of fluid mechanics, there was a sequence of discoveries of PDEs which possess infinitely many (and often non-obvious) symmetries, and for which there exist methods of quadrature for all solutions. These discoveries have been very influential over the past three decades, and have been shown to be connected to a broad range of other subjects in mathematics.
Completely integrable systems are special, nonetheless, so the developments over the past decade of perturbation methods akin to KAM theory for Hamiltonian systems with infinitely many degrees of freedom, in particular PDE, are very natural. This workshop will provide a cross-section of the fields of Hamiltonian PDE, including:

(1) modern developments in techniques of integrability, both algebraic and more analytically based,
(2) refined asymptotics of integrable systems in the small dispersion limit or other singular limits,
(3) extension of techniques of quadrature, including elements of inverse spectral theory and random matrix theory,
(4) KAM theory for PDE and other Hamiltonian systems possessing infinitly many degrees of freedom, and
(5) Nekhoroshev stability theory and Arnold diffusion in infinite dimensional systems.

Confirmed Speakers:

Simonetta Abenda (Università di Bologna)
Dario Bambusi
(Università degli Studi di Milano)
Massimiliano Berti (SISSA, Trieste)
Roy Choudhury (University of Central Florida)
Percy Deift (CIMS)
Hakan Eliasson (Université Paris 7)
Benoît Grébert (Université de Nantes)
John Harnad (CRM & Concordia University)
Eduard-Wilhelm Kirr (University of Chicago)
Sergei Kuksin (Heriot-Watt University)
Nader Masmoudi (CIMS)
Alexander Mikhailov (University of Leeds)
Maung Minoo (McMaster University)
N. Sri Namachchivaya (University of Illinois at Urbana-Champaign)
Jürgen Pöschel (Universitat Stuttgart)
David Sattinger (Yale University)
Michael Sigal (Notre Dame & University of Toronto)
Jacek Szmigielski (University of Saskatchewan)
Alexander Tovbis (University of Central Florida)
Stephanos Venakides (Duke University)
Vitali Vougalter (McMaster & The Fields Institute)
Eugene Wayne (Boston University)
Doug Wright (McMaster & The Fields Institute)
Yingfei Yi (Georgia Institute of Technology)
Jiangong You (Nanjing University)
Xin Zhou (Duke University)

Back to top