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Link Nomenclature, Random Grid Diagrams, and Markov Chain Methods in Knot Theory.

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Speaker: Shawn Witte, UC Davis
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Location: 2112 Mathematical Sciences Building
Start time: Fri, Dec 13 2019, 2:10PM

I provide a method for selecting a canonical link isotopy class for 2-component links using writhe trends of the link which are obtained from Markov chain Monte Carlo sampling. Then I provide some combinatorial results exploring the properties of grid diagrams of links. The Frisch-Wasserman-Delbruck conjecture is proven for random grid diagrams of knots which states that the probability of obtaining the unknot from a random 1-component grid diagram goes to 0 as grid size increases. I then explore Markov chain methods, namely the Wang-Landau algorithm, for grid diagrams and give results regarding the rate of decay of the unknotting probability as well as some writhe data for grid diagrams.

This is Shawn’s exit seminar