My research focuses on using Heegaard Floer homology to answer questions in low-dimensional topology.

Publications and Preprints

  1. Involutive Heegaard Floer homology and rational cuspidal curves
    with M. Borodzik. Submitted, 2017.
  2. A note on surgery obstructions and hyperbolic integer homology spheres
    with T. Lidman. Submitted, 2017.
  3. Satellite knots and L-space surgeries
    Bulletin of the London Mathematical Society
  4. A survey on Heegaard Floer homology and concordance
    Tim Cochran Memorial Volume, JKTR Vol. 22, Iss. 2.
  5. A note on positive definite, symplectic manifolds
    with T. Lidman.
    To appear in Journal of the European Mathematical Society
  6. Cable links and L-space surgeries
    with E. Gorsky.
    To appear in Quantum Topology
  7. The Alexander module, Seifert forms, and categorification
    with T. Lidman and L. Watson.
    Journal of Topology Vol. 10, Iss. 1, 22-100
  8. Surgery obstructions and Heegaard Floer homology
    with C. Karakurt and T. Lidman.
    Geometry & Topology 20 (2016), 2219-2251
  9. A note on the concordance invariants epsilon and upsilon
    Proceedings of the American Mathematical Society
  10. Berge-Gabai knots and L-space satellite operations
    with T. Lidman and F. Vafaee.
    Algebraic & Geometric Topology 14 (2014), Iss. 6, 3745-3763
  11. Four-ball genus bounds and a refinement of the Ozsvath-Szabo tau-invariant
    with Z. Wu.
    Journal of Symplectic Geometry Vol. 14, No. 1 (2016), 305-322
  12. An infinite rank summand of topologically slice knots
    Geometry & Topology 19 (2015), 1063-1110
  13. Reducible surgeries and Heegaard Floer homology
    with T. Lidman and N. Zufelt.
    Mathematical Research Letters, Vol. 22 (2015), Iss. 3
  14. On the knot Floer filtration of the concordance group
    with S. Hancock and M. Newman.
    Journal of Knot Theory and Its Ramifications, Vol. 22, Iss. 14
  15. On the concordance genus of topologically slice knots
    International Mathematics Research Notices Vol. 2015, Iss. 5, 1295-1314
  16. Bordered Floer homology and the tau-invariant of cable knots
    Journal of Topology Vol. 7, Iss. 2, 287-326
  17. The knot Floer complex and the smooth concordance group
    Commentarii Mathematici Helvetici Vol. 89, Iss. 3, 537-570
  18. A note on cabling and L-space surgeries
    Algebraic & Geometric Topology 11 (2011), Iss. 1, 219-223
  19. Discriminative topological features reveal biological network mechanisms
    with M. Middendorf, E. Ziv, C. Adams, L. Chen, R. Koytcheff, C. Levovitz, G. Woods, and C. Wiggins. BMC Bioinformatics 2004, 5:181 2004, 5:181