Hass will speak on:
Title: Width invariants and the physical motion of curves through a medium
Abstract: The method of gel electrophoresis was developed in the 1970s to separate fragments of DNA as they migrate through a gel, a porous sponge-like medium. An electric current pulls smaller molecules faster than larger ones. When the molecules are closed loops of DNA, biologists believe that the motion is determined by the “average crossing number”. However other knot invariants may be relevant to such motion. We define and compute some of these, and relate them to other knot invariants. This is joint work with Hyam Rubinstein and Abigail Thompson.
Vertesi’s talk will be:
Title: Transverse positive braid satelites
Abstract: In this talk I investigate transverse knots in the standard contact structure on R^3. These are knots for which y>dz/dx. The name “transverse” comes from the fact that these knots are positively transverse to the contact planes given by the the kernel of the 1-form dz−ydx. The classification of transverse knots has been long investigated, and several invariants were defined for their distinction, one classical invariant is the self-linking number of the transverse knot, that can be given as the linking of the knot with its push off by a vector field in the contact planes that has a nonzero extension over a Seifert surface. Smooth knot types whose transverse representatives are classified by this classical invariant are called transversaly simple. In this talk I will talk about how transverse simplicity is inherited for positive braid satelites of smooth knot types.