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Joanna Nelson : Invariants of contact structures and Reeb dynamics

Contact geometry is the study of geometric structures on odd dimensional smooth manifolds given by a hyperplane field specified by a one form which satisfies a maximum nondegeneracy condition called complete non-integrability; these hyperplane fields are called contact structures. The associated one form is called a contact form and uniquely determines a vector field called the Reeb vector field on the manifold. Contact and symplectic geometry are closely intertwined and we explain how one can make use of J-holomorphic curves to obtain contact invariants. This talk will have lots of examples, cool pictures, and animations illustrating these fascinating concepts in contact geometry.

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