Colloquium
Fri, 14 April, 2017
5:00pm
Title: Rotational symmetries of knots
Speaker: Swatee Naik, University of Nevada and NSF
Abstract: Knots are circles embedded in the three dimensional sphere. Periodic knots, such as the overhand or trefoil knot, are invariant under a rotation, and this symmetry can be easily illustrated in a knot diagram drawn in the plane. It so happens that the orbit space is also a three-sphere, in which the image of a periodic knot is called a quotient knot. Many properties of periodic knots are a direct consequence of the branched covering set up that occurs between various three-manifolds that are naturally associated with the periodic knot and the quotient knot, respectively.
In this talk we will begin with definitions and examples, introduce the basics of the theory, and demonstrate how properties of periodic knots can be used to detect knots that are not periodic. Our tools will include knot polynomials, homology of branched covers, and Heegaard-Floer correction terms.
Short Bio: Dr. Swatee Naik is a Professor at the University of Nevada, Reno and currently a program director at the National Science Foundation. Her area of research is knot theory and low dimensional topology. The draft of a book on Classical Knot Concordance is work in progress with Charles Livingston, and we welcome feedback. Swatee has served in administrative roles including vice chair and chair of the department and chair of the university faculty senate. At NSF, her main duties are in Topology and Geometric Analysis. She is involved in many other programs, such as Research Experience for Undergraduates, Graduate Research Fellowships, Postdoctoral Fellowships, Enriched Doctoral Training and NSF Research Traineeships.