A Chain of Knot Invariants by Zachary Romrell ’23, Mathematics Senior Thesis Defense

A Chain of Knot Invariants by Zachary Romrell ’23, Mathematics Senior Thesis Defense, Friday, May 12, 1 – 1:45 pm, North Science Building 015, Wachenheim.

Abstract:  Since the beginnings of knot theory, a crucial question has involved distinguishing two mathematical knots from one another.  A knot invariant is a quantity defined for a knot that does not depend on the particular embedding of the knot.  Therefore, by comparing the invariant values of one knot to another we can successfully tell two knots apart when their invariant values differ.  It turns out two of the more well-studied knot invariants: the bridge number and braid number are the lower and upper bounds in a sequence of knot invariants that bound one another.  We will further explore a new mathematical object that can be constructed from a knot conformation that allows us to analyze all of these invariants at the same time.