Research

My research interests are in low dimensional topology and geometry, especially knot theory. Though the focus is topological in nature (often on knots!), the techniques sometimes involve things like homological algebra, combinatorics or graph theory. I'm also interested in broader applications of topology.

I completed my Ph.D. in May 2013 under the direction of Cameron Gordon.

Papers

Symmetric unions without cosmetic crossing changes.
Accepted by Springer, AWM Research Symposium Proceedings. arXiv, PDF

Cosmetic surgery in L-spaces and nugatory crossings.
with Tye Lidman, 2015. Accepted by Transactions of the AMS. arXiv, PDF.

Montesinos knots, Hopf plumbings, and L-space surgeries.
with Kenneth L. Baker, 2014. Submitted. arXiv, PDF

Pretzel knots with L-space surgeries. MMJ, arXiv, PDF
with Tye Lidman. Michigan Mathematical Journal 65 (1) (2016) 105-130.

Genus two mutant knots with the same dimension in knot Floer and Khovanov homologies. AGT, arXiv, PDF
with Laura Starkston, Algebraic & Geometric Topology 15 (2015) 43–63.

Behavior of knot Floer homology under Conway and genus two mutation. PhD Dissertation, The University of Texas at Austin, May 2013. Dissertation repository

Selected talks

Nugatory crossings and cosmetic surgery in L-spaces
Colloquium, University of Alabama, Tuscaloosa, AL, February 2016

The cosmetic crossing conjecture and nugatory crossings
Joint Meetings of the AMS/MAA, Seattle, WA, January 2016

Cosmetic surgery in L-spaces and nugatory crossings
Tech Topology Conference, Georgia Tech, Atlanta GA, Dec 2015

Cosmetic surgery in L-spaces and nugatory crossings.
Special Session on Invariants of Knots, Links and 3-Manifolds, AMS Sectional Meeting, Rutgers, NJ, November 2015

Cosmetic surgery in L-spaces and nugatory crossings.
Geometry and Topology Seminar, MSU, East Lansing, MI, November 2015

Cosmetic surgery in L-spaces and nugatory crossings.
Topology Seminar, University of Texas, Austin, TX, September 2015

Cosmetic surgery in L-spaces and nugatory crossings. PDF
Workshop in Geometric Topology, TCU, Fort Worth, TX June 2015

Cosmetic crossing changes in thin knots.
Moab Topology Conference, Moab, UT, May 2015

Cosmetic crossing changes in thin knots.
Symplectic Geometry, Gauge Theory, and Categorification Seminar, Columbia University, NY, May 2015

Cosmetic crossing changes in thin knots.
AWM Research Symposium, University of Maryland, Baltimore, MD, April 2015

Cosmetic crossing changes in knots
Special Session on Knot Theory and Floer-Type Invariants, AMS Sectional Meeting, East Lansing, MI, March 2015

Montesinos knots, Hopf plumbings, and L-space surgeries. PDF
Special Session on Knot Theory, Joint Meetings of the AMS/MAA, San Antonio, TX, January 2015

Montesinos knots and L-space surgeries.
Colloquium, Sam Houston State University, Huntsville, TX, October 2014

Montesinos knots, Hopf plumbings and L-space surgeries. PDF
Special Session on Interactions between Knots and Manifolds, AMS Sectional Meeting, San Francisco, CA, October 2014

Montesinos knots and contact structures. PDF
Special Session on Invariants in Low-Dimensional Topology, AMS Sectional Meeting, Baltimore, MD, March 2014

Pretzel knots admitting L-space surgeries and questions about mutation.
Geometry and Topology Seminar, Caltech, Pasadena, CA, November 2013

Pretzel knots admitting L-space surgeries.
Geometry and Physics Seminar, University of Miami, Miami, FL, November 2013

Pretzel knots admitting L-space surgeries. PDF
Special Session on Geometric Topology of Knots and 3-Manifolds, AMS Sectional Meeting, Philadelpha, PA, October 2013

Pretzel knots admitting L-space surgeries.
Topology Seminar, Rice University, Houston, TX, September 2013

Mutation and total dimension in knot Floer homology.
Colloquium, Rice University, Houston, TX, September 2013

Pretzels knots admitting L-space surgeries.
Rolfsenfest, CIRM, Luminy, France, July 2013

Mutation and knot Floer homology
Colloquium, University of Nevado at Reno, May 2013

Thesis defense.
Topology Seminar, University of Texas, April 2013

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