Research

My research interests include knot theory, Floer homology, mutation and other areas of low-dimensional topology and its applications.

Papers

Pretzel knots and essential Conway spheres in knot Floer homology.
With Tye Lidman, 2013; preprint available upon request.

Genus 2 mutant knots with the same dimension in knot Floer and Khovanov homologies.
With Laura Starkston, 2012, submitted to AGT; in revisions. arXiv,  PDF

The topology of finite graphs and the Hanna Neumann conjecture.
Expository Undergraduate Thesis, 2006.

Selected talks

The total rank conjecture in knot Floer homology. PDF
Joint Meetings, San Diego, CA, 2013

Knot homology invariants and genus 2 mutation. PDF
Topology Students Workshop, Georgia Tech, GA, June 2012

Genus 2 mutation of knots.
Joint Meetings, Boston, MA, January 2012

The link surgeries spectral sequence.
Heegaard Floer Seminar, University of Texas, Austin TX, March 2012

Mutation of knots in manifolds.
GSTGC, Michigan State University, Lansing, MI, April 2011

The Jones polynomial of knots.
Trinity University, San Antonio, TX, March 2011

Mapping cones and homology theories.
Junior Topology Seminar, University of Texas, Austin TX, April 2010

Combinatorial Knot Heegaard Floer Homology (Candidacy Exam). PDF
Junior Topology Seminar, University of Texas, Austin TX, May 2009

Computations with Heegaard Floer Homology. PDF
Junior Topology Seminar, University of Texas, Austin TX, November 2008

Click here for a complete list of seminar talks and conferences attended