Topology Seminar- Complexity of computing Khovanov homology of closed n-braids

Tue, 4 February, 2020 9:45pm

Speaker:Marithania Silvero (Universidad de Huelva, Spain)
Date and time: Tuesday, February 4, 4:45--6:00pm
Place: 1776 G Street C119
Title: Complexity of computing Khovanov homology of closed n-braids
Abstract: .Khovanov homology is a link invariant which categorifies Jones polynomial. In general, computing Jones polynomial (so also Khovanov homology) is NP-hard. However, if we consider a closed braid of fixed number of strands, it is well-known that all classical quantum invariants (in particular Jones polynomial) can be computed in polynomial time. We conjecture that the complexity of computing Khovanov homology of a closed braid of fixed number of strands, is polynomial with respect to the number of crossings. In this talk we show some advances on the conjecture, showing that the result holds when considering extreme Khovanov homology of closed braids on 3 and 4 strands. This is an ongoing project.

 


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