Research

Generally I work in the intersection of algebra and topology. I am motivated by questions arising from knot theory, but I prefer to give algebraic answers to the questions. I like to study maps between things, so I am naturally drawn to representation theory (mostly of the braid groups), finite type invariants, planar algebras, and quantum computing. 

Here is my CV.

Here is a link to my ArXiv papers.

Here are my papers:

Danceability, a new definition of bridge index joint with Sol Addison, Lila Snodgrass and Everett Sullivan

Searching for Order Preserving Braids Algorithmically  joint with Jonathan Johnson and Hannah Turner

Computing Finite Type Invariants Efficiently  join with Dror Bar-Natan, Itai Bar-Natan and Iva Halacheva

Danceability,_Directed_by_Braid_Index_  joint with Sol Addison and Lila Snodgrass

The quotients of the Braid Groups by Their Congruence Subgroups  joint with Wade Bloomquist and Peter Patzt

Large 1-Systems of Curves in Non-Orientable Surfaces joint with students Sarah Ruth Nicholls and Julie Shneidman as part a summer REU project.

Yarn Ball Knots and Faster Computations, joint with Dror Bar-Natan, Itai Bar-Natan and Iva Halecheva

 

An Invariant of Virtual Trivalent Spatial Graphs, joint with Sherilyn Tamagawa and Evan Carr

Finite Image Homomorphisms of the Braid Group and its Generalizations  Joint with Yvon Veberne

   OC relation— A quick proof of a known fact that the OC  relation can be written in two ways.

Ribbon 2-Knots, 1+1=2, and Duflo’s Theorem for Arbitrary Lie Algebras  joint with Dror Bar-Natan and Zsuzsanna Dancso

PhD Thesis: Discrete Representations of the Braid Groups

Complete Classification of Discrete Specializations of the Burau Representation of B_3

A Survey of Grid Diagrams and a Proof of Alexander’s Theorem

My Master’s thesis: The Alexander Polynomial

Turning Math Into Dance: Lessons from Dancing my PhD