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Knot Floer homology and the Upsilon function

Date: Wednesday, June 07, 2017 13:45 - 15:45
Speaker: Andras Stipsicz (Alfréd Rényi Institute of Mathematics)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Formal Sciences Seminar
Host: Tamas Hausel
Lab building west seminar room

Abstract:

Knot Floer homology (an invariant discovered by Peter Ozsvath and Zoltan Szabo around 2001) provides a number of invariants to study knots, links, and relations among them. The knot Floer chain complex (a slightly complicated algebraic object associated to a knot by the theory) can be used to define these numerical invariants. More recently, in a joint project with P. Ozsvath and Z. Szabo, we found a piecewise linear continuous function (the Upsilon-function of the knot) determined by the knot Floer chain complex. In the lecture I plan to review the most important knot invariants, starting with the Alexander polynomial. After the description of the knot Floer chain complex, I will outline the definition of the Upsilon function, and will present some simple applications.
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