Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
Geometry and Topology Seminar: Knotted fields and real algebraic links
In order to implement knotted configurations in physical systems it is often very useful to have an explicit function, ideally a polynomial, f:R^3 -> C with a zero level set of given knot type. In this talk I will introduce an algorithm that for every link L constructs a polynomial f:R^4 -> R^2 whose zero level set on the unit three-sphere is L. Applying stereographic projection then makes these functions applicable to physical systems.
This constructive approach allows us to prove several results about the functions and their knotted zero level sets, for example under which conditions f can be taken to have an isolated singularity or when arg f is a fibration of the link complement over S^1.
Contact Andrew Lobb for more information