My research interests include knot theory, Floer homology, mutation and other areas of low-dimensional topology and its applications.
Pretzel knots and essential Conway spheres in knot Floer homology.
With Tye Lidman, 2013; preprint available upon request.
The topology of finite graphs and the Hanna Neumann conjecture.
Expository Undergraduate Thesis, 2006.
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