Nicholas Connolly

Email: nicholas.connolly@inria.fr

Background

I am currently working at Inria in Paris, France on a postdoc. My project is related to quantum error correction. I received a PhD in mathematics from the University of Iowa in 2021. My research focused on knot theory and 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 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. In particular, I am using graph theory to classify non-algebraic tangle diagrams.

 

Links

2-String Tangles Database

Curriculum Vitae

Research Statement

GitHub

 

Recent Presentations

Fall 2020 SCMB Poster Presentation: A Database of Tangles: Knot Theoretic Models for DNA Topology

Summer 2020 presentation on NSF MSGI research internship: Multi-Modal Community Detection with Multi-Weighted Graphs

Fall 2019 presentation on generalized planar diagram notations for tangles: Constellations and an Algebraic Planar Diagram Code

ACML 2019 poster presentation on summer research in machine learning: Using Artifical Intelligence to Automate Body Movement Analysis (short paper)

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

Summer 2014 research in coding theory: Constructing Linear Codes with Record Breaking Parameters