Abstract:

Apart from being very popular with fishermen and climbers, knots are rich mathematical objects, whose classification is still of great interest. Classifying different knots comes down to defining invariants, which can be as easy as the crossing numbers or as complicated as homology theories. In this talk, we quickly go through the basics of knot theory and define a very powerful recent invariant, Knot Floer Homology, which was introduced by Ozsváth and Szabó and independently by Rasmussen. Time-permitting we will delve into the details of the Ozsváth-Szabó construction of this invariant, whose approach is more combinatorial and allows it to be calculated by a computer program.

Video: