The Average Genus of Oriented Rational Links

May 17, 2022

Categories: Dissertation Defense Tags: Mathematics (Applied)

Doctoral Candidate Name: Dawn Ray
Program: Mathematics (Applied)
Defense Date and Time: June 30, 2022 – 1:00 PM
Defense Location: Zoom meeting
Committee chair’s Name: Yuanan Diao
Committee Members: Gabor Hetyei, William Brian, Anthony Brizendine
Abstract:

The goal of this thesis is to enumerate the number of oriented rational knots and the number of oriented rational links with any given crossing number and minimum genus. This allows us to obtain a precise formula for the average minimal genus of oriented rational knots and links with any given crossing number.