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Graduate Workshop on Symplectic and Contact Topology, October 15 -19, 2012

Workshop on Symplectic and Contact Topology – Fall 2012

Organized by Mohammed Abouzaid and Yakov Eliashberg

This graduate student workshop will be associated with the program in Symplectic Topology at the Center during the Fall of 2012. The workshop will be organized by Yakov Eliashberg and Mohammed Abouzaid (both in residence at the Center for the Fall semester). There have been tremendous advances in Symplectic Topology and Contact Topology over the last 10 years with the introduction of Floer theory and symplectic field theory. Symplectic (co)homology is one of the simplest invariants to arise out of these deveopments, and has, since its introduction, been responsible for several breakthroughs in symplectic topology (construction of exotic symplectic structures and study of Lagrangian embedding), contact dynamics (Weinstein conjecture on the existence of Reeb orbits) and mirror symmetry (construction of mirrors of Lie group action).  The goal of this workshop is to introduce graduate students to developments in the study of the symplectic topology of Stein manifolds via pseudo-holomorphic curves, with a focus on symplectic cohomology.  The first part of the workshop will consist of student lectures about the basics of holomorphic curves and Floer homology, culminating in the construction of symplectic cohomology, and its computation in the simplest examples.  These lectures will be followed by lectures by the organizers and others senior mathematicians in residence who will provide perspective on the applications of the theory, and its interaction with related mathematical fields.

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Workshop on Symplectic and Contact Topology Schedule

Time Title Presenters
09:00am The Geometry of Liouville Domains Tobias Sodoge video
10:15am The Conley-Zehnder Index Corrin Clarkson video
11:30am Hamiltonian Floer Cohomology Jonathan Hanselman video
01:30pm Continuation Maps in Hamiltonian Floer Theory Krzysztof Putyra video
02:45pm Quantitative Symplectic Cohomology Kristen Hendricks video
04:15pm The Construction of Symplectic Cohomology Andre Carneiro video


Time Title Presenters
09:00am Weinstein Manifolds 101 Elizabeth Goodman video
10:15am Symplectic Cohomology of the Ball Alex Zamorzaev video
11:30am Kunneth Formula for Symplectic Homology Khoa Nguyen video
01:30pm Product on Symplectic Cohomology Heather Lee video
02:45pm BV Structure and Higher Operations Zack Sylvan video
04:15pm S^1 Equivariant Cohomology Joanna Nelson video


Time Title Presenters
09:00am Symplectic Cohomology of Cotangent Bundles and Legendre Transformation Erkao Bao video
10:15am Morse Homology on Loop Space Heather Lee video
11:30am Isomorphism between the Morse and the Floer Complex and Fredholm Theory for M^{+}(q,x): Dongning Wang/Jie Zhao video
01:30pm Liouville Domains and Sub-domains Nate Bottman video
02:45pm The Viterbo Transfer Map I: Construction Netanel Blaier video
04:15pm The Viterbo Transfer Map II: Properties and Applications Ailsa Keating video


Time Title Presenters
09:00am Computations of Symplectic Homology for Weinstein Manifolds I,II,III Yakov Eliashberg video
10:15am Computations of Symplectic Homology for Weinstein Manifolds I,II,III Yakov Eliashberg video
11:30am Computations of Symplectic Homology for Weinstein Manifolds I,II,III Yakov Eliashberg video
01:30pm Legendrian Contact Homology Lenny Ng video
02:45pm Knot Contact Homology and Physics Lenny Ng video
04:15pm Discussion and Questions


Time Title Presenters
09:00am Symplectic Cohomology and Fukaya Categories I,II Mohammed Abouzaid video
10:15am Symplectic Cohomology and Fukaya Categories I,II Mohammed Abouzaid video
11:30am Loose Legendrian Knots Emmy Murphy video