Monday, February 11th
Speaker: Louis H. Kauffman, University of Illinois at Chicago
Title: Introduction to Virtual Knot Theory
Meet the Speaker: 4:00 p.m., Cuneo Hall 312
w/ tea & cookies
Classical knot theory is a topological study of embeddings of closed curves in three dimensional space. As such, it models the knotting of closed loops of rope in ordinary Euclidean space. Classical knot theory is the same as the study of knots in a thickened two dimensional sphere. Knottheorists are interested in the way knots can wind around in any three-dimensional space. One of the next and most interesting cases is to studyknots in thickened surfaces such as thickenings of the torus or, more generally thickenings of a sphere with a number of handles attached to it. When knots occur in thickenings of surfaces other than the two dimensional sphere, it is natural to ask which surfaces can support a given knot, thus stabilizing the theory by adding and subtracting handles from the surface. In this talk, I will introduce the subject of virtual knots, where we use this stabilization. There is a diagrammatic theory for virtual knots quite similar to the diagrammatic theory for classical knots. We will introduce this subject, and its many surprising phenomena living at the interface between algebra and topology.
About the Speaker:
Louis Kauffman is Professor of Mathematics at the University of Illinois at Chicago. He is well-known for the bracket state sum model for the Jones polynomial, for a two variable link polynomial called the Kauffman polynomial and for the introduction and exploration of an extension of classicalknots called virtual knot theory. Kauffman is the author of four books on knot theory and the editor of the World-Scientific ‘Book Series On Knotsand Everything’ and the Editor in Chief and founding editor of the Journal of Knot Theory and Its Ramifications.
For More Information: http://www.luc.edu/math/ucms/