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Symplectic Geometry and PhysicsIPAM Spring 2003March 17 - June 13, 2003Scientific CommitteeValentin Afraimovich (Mexico) Program Schedule
Scientific OverviewSymplectic 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, ploasma physics, and others. ApplicationWe are no longer accepting applications for financial support to the SGP long program. You may still register or apply for financial support for the individual workshops. Please go to the appropriate workshop links. Orientation DayMarch 17, 2003Culminating Workshop at Lake ArrowheadJune 8 - 13, 2003This workshop will include resident participants at the junior and senior levels and will explore new directions and approaches of research in the fields discussed throughout the program. At this final event of the program the focus is on interactions between the junior and senior participants and developing future directions for collaborations. The conference will be held at Lake Arrowhead Conference Center, a mountain resort facility owned by UCLA ideally designed to such purposes. Attendance at this conference is limited to invited participants. Contact Us:Institute for Pure and Applied Mathematics (IPAM) |
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