Symplectic geometry originated as a mathematical outgrowth of Hamiltonian mechanics and dynamical systems and their applications to the theory of elementary particles, oceanographic and atmospheric sciences, condensed matter, accelerator and plasma physics and other disciplines at the classical and quantum levels. Ideally, a good mathematical model for the very complex systems listed above should describe the global information regarding the phase structure by means of relevant parameters rather than describing the existence of a specific solution of the equations of motion. A suitable mathematical framework, reflecting the complexity of these real world problems was pioneered in the works of Arnold, Gromov, Zehnder (and the whole Bochum school) and Eliashberg.
This program aims to revitalize the connection of mathematics to Hamiltonian mechanics and dynamical systems and to their applications in the theory of elementary particles, oceanographic and atmospheric sciences, condensed matter, accelerator and plasma physics and other disciplines at both the classical and quantum levels. Some particular questions of current interest that we hope to discuss are:
1) Define new stronger invariants in symplectic and contact geometry using monodromy actions.
2) Achieve a better understanding of the structure of Lagrangian submanifolds and using it in order to study chaotic kinetics.
3) Understand the structure of Fukaya category and its applications to mirror symmetry.
4) Use the filtration theory of Fukaya category.
5) Phase space topology of the chaotic Hamiltonian dynamics and its connection to the particle kinetics and transport. Application will be considered to the resonances, dynamical invariants, intermittency in the areas of particle advection, underwater acoustics, atom-photon interaction, plasma physics, and others.
(Universidad Autonoma de San Luis Potosi, Mexico)
Denis Auroux (Massachusetts Institute of Technology, Mathematics)
Fedor Bogomolov (New York University, CIMS)
Simon Donaldson (Imperial College, Mathematics)
Ludmil Katzarkov (University of California, Irvine, Mathematics)
Gang Liu (UCLA, Mathematics)
Tony Pantev (University of Pennsylvania, Mathematics)
George Zaslavsky (New York University, Physics and Mathematics)