Boston Graduate Topology Seminar

MIT Meeting

Saturday, November 13, 9:30AM-12:15PM

Math Department, 4th Floor Lecture Room (Building 2, Room 449)

Speakers:

9:30-10:15: Allison Moore (Virginia Commonwealth University)

Title: Tangle decompositions and immersed curves

Abstract: A tangle decomposition along a Conway sphere breaks a knot or link into simpler pieces, each of which is a two-string tangle. In this talk, we'll discuss (some of the ways) in which Khovanov homology can be approached and calculated using tangle decompositions. In particular, the algebraic invariants associated with tangles can be translated into sets of immersed curves on the four-punctured sphere. This strategy turns out to be quite useful for investigating two classic open problems: the cosmetic surgery conjecture and the cosmetic crossing conjecture. This is joint with Kotelskiy, Lidman, Watson and Zibrowius.

10:30-11:15: Joshua Wang (Harvard)

Title: Khovanov homology, split links, and band surgeries

Abstract: Lipshitz and Sarkar recently proved that Khovanov homology detects split links. Interestingly, their detection result is only true when taken in a ring of characteristic 2. I'll explain a related but different way in which Khovanov homology can "see" splitness of a link that works for any coefficient ring. The approach uses band surgeries and is related to the cosmetic crossing conjecture. I'll also describe a generalization from Khovanov homology (N = 2) to sl(N) link homology.

11:30-12:15: Hyunki Min (MIT)

Title: Cabling Legendrian knots

Abstract: Legendrian knots play an important role in 3-dimensional contact geometry since they have many implications, such as contact surgeries, open book decompositions and Heegaard Floer homology, as well as applications to links and braids. In this talk, we will discuss the classification of Legendrian knots. In particular, we will completely describe Legendrian representatives of positive cable knots in terms of the underlying knot type. This is a joint work with Apratim Chakraborty and John Etnyre.

Location:

The Mathematics Department is located in Building 2. See Directions and Campus Map.