Department of Mathematics

Colloquium

  •  An introduction to Heegaard Floer homology
  •  03/20/2017
  •  5:30 PM - 6:30 PM
  •  
  •  Peter Ozsvath, Princeton

'Knot theory' is the study of closed, embedded curves in three-dimensional space. Classically, knots can be studied via a various computable polynomial invariants, such as the Alexander polynomial. In this first talk, I will recall the basics of knot theory and the Alexander polynomial, and then move on to a more modern knot invariant, 'knot Floer homology', a knot invariant with more algebraic structure associated to a knot. I will describe applications of knot Floer homology to traditional questions in knot theory, and sketch its definition. This knot invariant was originally defined in 2003 in joint work with Zoltan Szabo, and independently by Jake Rasmussen. A combinatorial formulation was given in joint work with Ciprian Manolescu and Sucharit Sarkar in 2006.

 

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Michigan State University
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