Neighbors of Knots in the Gordian Graph

Switching a crossing on a knot diagram is one of the simplest methods for converting one type of knot into another type of knot. The Gordian graph is the graph which keeps track of which knot types can be converted into which other knot types by a single crossing change. Associate Professor of Mathematics Scott Taylor will show, using arguments that are almost entirely elementary, that each vertex of the Gordian graph is adjacent to a vertex having arbitrarily high bridge number and bridge distance. This is joint work with Ryan Blair, Marion Campisi, Jesse Johnson, and Maggy Tomova.