Date: Tuesday Feb 10, 2026

Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)

Title: Mutation Invariance of Khovanov Homology

Speaker: Susan Rutter

Abstract: I will cover Stephan Wehrli's 2009 paper on the mutation invariance of Khovanov Homology over F_2. This paper uses Bar Nathan's cobordism category for Khovanov homology, of which I will do a short review.

References:

• Mutation Invariance of Khovanov Homology by Dror Bar-Natan
• Mutation Invariance of Khovanov Homology over FF_2 by Stephan Wehrli

Date: Tuesday Mar 3rd, 2026

Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)

Title: What you see is what you get, if you alternate!

Speaker: Ipsa Bezbarua

Abstract: Historically, alternating links have been found to display very interesting properties. So much so that Ralph Fox even poised the question "What is an alternating knot?", meant to be answered in terms of the knot complements. In his PhD thesis, Menasco proved some extremely important theorems related to alternating links. In this talk, we will learn about two of these. First, we will see that an alternating link is prime if and only if its diagram representation is prime. We will also see that if an alternating link is not a torus link, its complement must admit a complete hyperbolic metric.

References:

• Closed incompressible surfaces in alternating knot and link complements by W. Menasco