Topology Seminar-Trivalent Graphs and Virtual Links
Fri, 2 October, 2020
5:00pm
The Greater (George) Washington Topology Seminar will be starting next week. This seminar is meant for students and faculty who work at universities in the Greater Washington Area and are interested in topology and knot theory. The seminar will take place on Fridays from 1pm to 2pm EDT and will be held virtually via Zoom. The following is a list of confirmed speakers and dates for the seminar:
1. October 2, 2020: Louis H. Kauffman (University of Illinois at Chicago)
2. October 9, 2020: Charles Frohman (University of Iowa)
3. October 16, 2020: Thang T. Q. Lê (Georgia Institute of Technology)
4. October 23, 2020: Pierrick Bousseasu (ETH Zurich)
5. October 30, 2020: Micah Chrisman (Ohio State University)
5. November 13, 2020: Boštjan Gabrovšek (University of Ljubljana)
6. November 20, 2020: Razvan Gelca (Texas Tech University)
7. December 4, 2020: Helen Wong (Claremont McKenna College)
The first talk will be by Louis H. Kauffman and will take place on October 2, 2020.
Title: Trivalent Graphs and Virtual Links
Abstract: This talk is joint work with Scott Baldridge and Willam Rushworth. We define a correspondence be- tween trivalent virtual graphs (trivalent ribbon graphs) and virtual link diagrams (abstract link diagrams) so that it is seen that a generalization of the Penrose evaluation for three-coloring trivalent graphs corre- sponds to the Kauffman bracket polynomial. The generalization of the Penrose evaluation is a polynomial depending on a perfect matching in the graph. Thus a graph with a perfect matching corresponds to a virtual link.
This leads to an interaction between graph theory and virtual link theory that allows us to examine many invariants across this relationship and to define integral Khovanov homology for trivalent graphs with perfect matchings.
The definition of Khovanov homology that we discuss is a new simplification of the integral Khovanov homology for virtuals originally defined by Manturov and further studied by Dye, Kaestner and Kauffman. The new version is also studied by Kauffman and Ogasa and by Baldridge, Kauffman and McCarty.
The Zoom information is listed below:
Topic: GW Topology Seminar
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