Graduate Student Seminar- Symmetric unions of knots.

Date: November 14, (Friday) 1-2 pm

Location: Phillips Hall 109

Speaker: Ben Clingenpeel, GWU

Title:  Symmetric unions of knots.

Abstract:Symmetric unions of knots were introduced by Lamm in 2000 as a generalization of an earlier construction due to Kinoshita and Terasaka. Every symmetric union is a ribbon knot, but the converse is currently open and we will discuss some of the recent work aimed at finding ribbon knots that do not admit symmetric union presentations. We will also explore the relationship between a symmetric union and its partial knots, the knots that can be used to present the symmetric union diagrammatically. When a symmetric union admits distinct partial knots, we call them symmetrically related. Lamm asked in 2021 whether all knots with the same determinant are symmetrically related, and we will answer this question in the negative. If time permits, we will show also that 'being symmetrically related' is not an equivalence relation. 

Graduate Student Seminar is mandatory for all math graduate students.