
I recently returned from a semester as part of the Knot Concordance and 4manifolds group of the
Junior Hausdorff Trimester Program in Topology at the Hausdorff Institute for Mathematics in Bonn, Germany, where I participated in learning seminars on filtrations of the knot concordance group, trisections, surgery theory, and the disc embedding theorem of Freedman. We also organized a
conference on 4manifolds and knot concordance from October 1721 2016.
While at UT I have helped to organize learning seminars in the basics of Heegaard Floer homology (with Andrew Lee) and on applications of Heegaard Floer homology to questions in 4manifold theory and knot concordance (with Lisa Piccirillo).
Research
My work can be found on the Arxiv:
Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance Joint with Mark Powell , 2017.
Our Maple program for computing the twisted Blanchfield pairing of a knot's 0surgery is here.
Knot traces and concordance Joint with
Lisa Piccirillo, 2017, submitted.
The topological sliceness of 3strand pretzel knots. 2016, to appear in Algebraic & Geometric Topology.
Ravels arising from Montesinos tangles. Joint with Erica Flapan, 2016, to appear in the Tokyo Journal of Mathematics.
A note on the topological sliceness of some 2bridge knots. 2015, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society.
Distinguishing mutant pretzel knots in concordance. Journal of Knot Theory and its Ramifications 26(07), 2017.
The Wecken property for random maps on surfaces with boundary Joint with Jacqueline Brimley, Matthew Griisser, and P. Christopher Staecker. Topology and its Applications 159, p. 36623676, 2012.
Teaching
I am currently the TA for M427L: Advanced Calculus for Applications II. I taught M408K: Differential Calculus in the spring of 2017 as an Assistant Instructor. I have previously TAed for M408C: Differential and Integral Calculus (Fall 2015, SI), M310P: Mathematics for Plan II Students (Spring 2014), and M408K: Differential Calculus (Fall 2013). I have also supervised projects in math education policy, algebraic topology, knot theory, and cryptography with UT's Directed Reading Program and Freshman Research Initiative and have run beginning and end of semester review sessions for the Sanger Learning Center . Last spring I helped organize a four day Mini Math Camp run by SMMG, a major outreach program of the department.