These talks are a short introduction to knot theory from a combinatorial point of view and with an eye towards applications to Natural Science. The talks are self-contained and form a short introductory course in knot theory.
3. Introduction to the Khovanov Homology via working with the bracket polynomial and cube categories and applications of Rasmussen invariant to reconnection numbers for knotted vortices. Discussion of other applications of knot theory and knot homology.