Conference: Topological and Quantitative Aspects of Symplectic Manifolds; Columbia University and Barnard College, March 17-20, 2016

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The purpose of this grant is to support roughly 27 junior participants, primarily graduate students and postdoctoral fellows, at the conference "Topological and quantitative aspects of symplectic manifolds" to be held at Columbia University and Barnard College on March 17-20, 2016. The conference will be organized by Mohammed Abouzaid, Ailsa Keating, Robert Lipshitz, Walter Neumann, and Lisa Traynor. The conference will feature 16-20 talks and roughly 80 participants.Symplectic geometry and contact geometry are the abstract setting of classical mechanics. Symplectic geometry was originally developed to study the Hamiltonian formulation of classical mechanics, with a particular focus on celestial mechanics. More recently, it has turned out that symplectic and contact geometry are key to fundamental questions in theoretical high energy physics, as a key component in string theory and with close relations to gauge theory. Roughly speaking, a symplectic manifold is a smooth space in which there is a well-defined notion of area - but not necessarily a well-defined notion of distance. One key question is how to tell if two symplectic manifolds are the same, and to list all symplectic manifolds with certain properties. Another important topic is the notion of size in symplectic manifolds, given that there is no intrinsic notion of distance. This problem is particularly subtle - it turns out, for instance, that an infinite cylinder may not be symplectically bigger than a finite one - and again is reflected in strange theoretical phenomena in physics. Another important topic in symplectic geometry - and most of mathematics - is symmetry: what symmetries can symplectic spaces have? Is it possible to classify all highly-symmetric symplectic spaces? A last theme is using smooth symplectic spaces to study singular spaces: smooth spaces are easier to analyze, but understanding what properties of singularities they reflect is subtle. This conference will bring together roughly 80 researchers on these topics, with a particular emphasis on recent developments and work by younger researchers, to exchange ideas and results on these basic research topics. The ultimate goal, naturally, is to promote the progress of science. A secondary goal is to highlight the many contributions of women to the field, to provide mentoring and support for women researchers who are just getting started and so promote diversity among mathematics researchers.The conference web page, with information about speakers and registration, ishttp://math.columbia.edu/mcduff70