Nicholas Connolly

Email: nicholas-connolly@uiowa.edu

Background

I am a fifth year graduate student in mathematics at the University of Iowa. My current research in knot theory focuses on the tabulation of 2-string tangles.

Graduate Research

My research is focused on the knot theoretic structures known as tangles. A tangle can be understood as a sphere embedded with multiple entwined strings. While a tangle is a three dimensional object, mathematicians study them using tangle diagrams, the projected shadow of a tangle onto a two dimensional surface. The primary way to study tangles is through exploring the combinatorics of tangle diagrams.

The goal of my research is to exhaustively tabulate and classify 2-string tangles up to a fixed crossing number. I am in the process of creating a database to enumerate the preferred constructions for known tangles together with their structural properties. Tangles can be divided into families based on their construction. Some families are well understood while others have not yet been classified uniquely. In addition to computationally constructing a database, I am also working to improve the theoretical description of these tangle families.

 

Links

2-String Tangles Database

Curriculum Vitae

GitHub

 

Recent Presentations

Fall 2019 presentation on searching for internship opportunities as a graduate student in mathematics: Exploring Industry as a Pure Mathematcian

Spring 2019 research on using graph theory to describe tangle diagrams: Describing Non-Algebraic Tangles with Graphs

Fall 2018 research in the computational construction of 2-string tangles: Tabulation and Classification of 2-String Tangles