This award will provide funding to organize a conference,``Symplectic and Poisson geometry in interaction with Algebra, Analysis and Topology'', celebrating four decades since the emergence of symplectic and Poisson geometry and their influence on major areas of mathematics. The conference focuses on recent important developments in symplectic and Poisson geometry, and the interactions of these fields with Analysis, Algebra, differential equations and low-dimensional topology. Specific topics covered by the talks will include: Taubes' recent proof of the Weinstein conjecture using Seiberg-Witten theory, recent progress in Lagrangian intersection theory, classical and quantum Yang-Baxter equations, Poisson and quantum groupoids, dynamical Weyl groups, q-deformed Casimir connections and Kazdhan-Lusztig functors. The conference will provide a forum to outline the recently found connections by Nicolai Reshetikhin, San Vu-Ngoc and others between integrable systems in symplectic and algebraic geometry and representation theory. Reshetikhin and Vu-Ngoc talks will also discuss the recent progress in the quantization of integrable systems from a more algebraic and a more geometric view point, respectively. Other topics covered in the conference will regard recent breakthroughs in relating geodesic flow to eigenfunctions, and Hitrik and Sjostrand's recent work on spectra of non-self adjoint operators in dimension two (which relies heavily on Alan Weinstein's famous work on spectra of Zoll surfaces). The talks by Tudor Ratiu and Jerrold Marsden will focus on applications of symplectic geometry to a wide problems in physics and engineering such as as fluid and plasma theory, liquid crystals and micropolar fluids.
The goal behind this conference is that of holding a high profile meeting to bring together world experts and junior researchers to discuss these current exciting interactions. The time of the conference (May 2010) coincides with the first year anniversary of Alan Weinstein?s retirement from UC Berkeley. Weinstein has been one of the most influential figures in symplectic geometry and analysis in the past forty years. His fundamental work has inspired many mathematicians and led to the development of central concepts in symplectic and Poisson geometry, as well as to the establishment of symplectic geometry as an independent discipline within mathematics. The conference will provide a forum to dicuss Weinstein's impact on geometry and mathematics at large. The last few decades have witnessed numerous spectacular interactions between symplectic geometry, analysis, low dimensional topology and partial differential equations leading to new understanding in fundamental problems of mathematics. Today symplectic geometry is an active, central branch of mathematics populated by deep results and connections with physics, low-dimensional topology, gauge theory, integrable systems, representation theory, group theory, semiclassical analysis and Lie groups. The main theme of the Conference is to illuminate the particular type of interactions which characterize the past forty years of developments in symplectic geometry. To this end the conference will have talks by leading experts, both junior and senior, describing the current state of the art of several of the most fundamental research problems in these areas. Symplectic and Poisson geometry are by now well established fields of research, and its language and techniques are being used in many areas of mathematics, theoretical physics, and engineering such as symmetric bifurcation problems, integrable systems, string theory, geometric phases, nonlinear control, nonholonomic mechanics and locomotion generation in robotics.
The NSF Grant DMS 0965738, held by Maciej Zworski (PI) andAlvaro Pelayo (co-PI) during 02/28/2010 --- 02/28/2011supported the organization of a major international conference``Symplectic and Poisson geometry in interaction with Algebra, Analysis and Topology'',at the Mathematical Sciences Research Institute in Berkeley, from May 4 -- 7 to 2010. Speakers and participants interacted overthe span of four days, and held numerous scientific discussions during the talks, andalso during the many breaks which separated the talks. With this NSF grant, we wereable to fund support the attendance of a number of advancedgraduate students and young mathematicians, for which the event was a uniqueopportunity to meet and interact with the leaders in their respective fields,hence establishingvaluable connections for their future academic career. Among the participantsthere were several women and members of underrepresented minorities. The meeting was an spectacular success and had a strong positive impact on thefield, and on the participants. A large number of the participants reported to ushow grateful they were to have been able to attend a conference in which abroad number of topics of high interest in mathematics and physics werecovered in a cohesive fashion. The conference also served as a platformto lay out key directions for future research in the field. Among the speakers, all of which were leading mathematicians,there were a number of members of the National Academy of Sciencesand plenary speakers at the International Congress of Mathematics.The speakers deliveredexcellent lectures takingcare of making their talks accessible to a broad audience, including advancedgraduate students. Our dissemination efforts were assisted by the fact thatall lectures were videotaped by the MSRI technical and support staff.All the lectures are available in the MSRI website: www.msri.org/web/msri/scientific/workshops/show/-/event/Wm514 The conference allowed several participants to establish collaborations withmathematicians slightly outside of their fields of research, and made it possible forgraduate students to establish contact with leading researchers in their fields.Our outreach efforts weregreatly enhanced by an amusing Public Lecture, which was expository in nature.This lecture was attended by a wide range of people, from young students withonly basic mathematical knowledge to senior professors inall areas of mathematics. The public lecture included lots ofpictures, photos, and amusing historical remarks whichmade it a delightful an encouraging event for young and oldalike to pursue mathematical research.
