Date: Tuesday Feb 16th & 23rd, 2021

Title: Fun with Virtual Knots

Speaker: Joe Boninger (CUNY GC)

Abstract: We give a brief introduction to the theory of virtual knots and links, introduced by Louis Kauffman in 1996. We will then prove Kuperberg’s fundamental theorem of virtual links: that every virtual link is uniquely representable, up to homeomorphism, by a link in a thickened surface such that the link complement contains no essential vertical annulus.

References

• Virtual knot theory by Kauffman
• What is a virtual link? by Kuperberg
• Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms by Carter, Kamada, Saito

Date: Tuesday Mar 23rd, 2021

Title: Constructions of color Khovanov homology

Speaker: Christine Ruey Shan Lee (University of South Alabama)

Abstract: Colored Khovanov homology is a categorification of the colored Jones polynomial which assigns a collection of bigraded homology groups whose graded Euler characteristic recovers the colored Jones polynomial. In this talk we will give an overview of the process of categorifying link polynomials and discuss the constructions for colored Khovanov homology by Cooper-Krushkal, Rozanksy, and Khovanov. We will conclude with how these constructions compare in the homotopy category of chain complexes.