Hello everyone,

Today in topology we have Christine Ruey Shan Lee from the University of South Alabama. Contact Henry if you are interested in going out to lunch with the speaker.

Her title and abstract are below:

Title: A surface construction for colored Khovanov homology

Speaker: Christine Ruey Shan Lee, University of South Alabama

Date: Feb 26, 2019

Time: 3:30 PM

Room: MSCS 509

Abstract: Colored Khovanov homology is a categorification of the colored Jones polynomial. To each integer n ≥ 2 and a diagram D of a link, it assigns a bigraded chain complex {C^{Kh}_{ i,j} (D, n)}. The graded Euler characteristic of the homology groups {H^{Kh}_{ i,j} (D, n)} gives the nth colored Jones polynomial. It has typically been difficult to extract topological information from colored Khovanov homology due to its dependence on the combinatorics of link diagrams. Inspired by Bar-Natan’s formulation of Khovanov homology for tangles and other approaches to topological formulations for Khovanov homology by McDougall and Seidel-Smith, we will give a construction of colored Khovanov homology of a knot in terms of embedded surfaces in the complement to more intrinsically motivate it using topology, and we will discuss potential applications.

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Neil R. Hoffman Assistant Professor Department of Mathematics 523 Math Science Building Oklahoma State University Stillwater, OK 74078-1058 405-744-7791 http://math.okstate.edu/people/nhoffman