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Mathematical Sciences Distinguished Colloquium by John Etnyre
Friday, Feb. 28
11 a.m. - noon Location: FN 2.106

John Etnyre

School of Mathematics
Georgia Institute of Technology

Invariants of embeddings and immersions via contact geometry

There is a beautiful idea that one can study topological spaces by studying associated geometric objects. More specifically one can associate to a manifold (that is a nice topological space) a symplectic or contact manifold (that is the geometric object). We will begin by looking at a classical and well-known theorem of Whitney concerning immersed curves in the plane and winding numbers. After an introduction to, and look back at the history of, contact geometry we will reinterpret Whitney's result in terms of contact geometry and then vastly generalize it to come up with invariants of any submanifold in a manifold. Focusing on the case of knots in Euclidean 3-space we will describe a long research program of Ekholm, Ng, Sullivan, and myself on knot contact homology, and more recent work of Ekholm, Ng, and Shende showing that knot contact homology is (more or less) a complete invariant of knots.

 

Persons with disabilities may submit a request for accommodations to participate in this event at UT Dallas' ADA website. You may also call (972) 883-5331 for assistance or send an email to [email protected]. All requests should be received no later than 2 business days prior to the event.
Contact Info:
Viswanath Ramakrishna, 972-883-6873
Questions? Email me.

Tagged as Lectures/Seminars, Professional Dev.
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