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.
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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.
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Date: Tuesday Mar 10th, 2026
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: What you see is what you get, if you almost alternate!
Speaker: Ipsa Bezbarua
Abstract: An almost alternating knot is one that is a crossing change away from being alternating. They share several properties in common with alternating knots. In this talk, we will see how to extend some of the results for alternating knots to almost alternating knots.
References:
Date: Tuesday Mar 17th, 2026
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: Braid Foliations and Markov's Theorem for the Unlink
Speaker: Emma Hasson
Abstract: In this talk we will explore the basic building blocks of braid foliations and see how they can be used to prove interesting things about braids with a foliation-based proof of Markov's theorem for the unlink.
Date: Tuesday Mar 24, 2026
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: Computing right-angled volume of alternating links
Speaker: Ilya Kofman
Abstract: Menasco and Thistlethwaite showed that a prime alternating link can be decomposed in only limited ways along Conway spheres into alternating tangles. From this decomposition, Champanerkar, Kofman and Purcell extracted a geometric link invariant, the "right-angled volume," as a sum of volumes of the associated hyperbolic right-angled ideal polyhedra. In this talk, we relate geometric, topological and combinatorial methods to compute the right-angled volume.
Date: Tuesday April 14th, 2026
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: What you see is what you get, if you almost alternate - part 2
Speaker: Ipsa Bezbarua
Abstract: An almost alternating knot is one that is a crossing change away from being alternating. They share several properties in common with alternating knots. In this talk, we will see how to extend some of the results for alternating knots to almost alternating knots.
References:
Date: Tuesday April 28th, 2026
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: Introduction to spectral sequences in equivariant cohomology
Speaker: Sriram Raghunath
Abstract: In this talk, we define the Borel equivariant cohomology for a space with a group action and explore the spectral sequences arising from this construction. We shall see the applications of this construction to classical equivariant topology as well as Khovanov homology.