Menu:

Research

My research program investigates topological, algebraic, and geometric methods in low-dimensional topology and smooth knot theory as applied to the category of Legendrian knots. I attempt to refine the ``geography'' of Legendrian knot theory by finding connections between new and existing knot invariants. Many of the objects involved are combinatorial in nature and open questions exist that are appropriate for undergraduate investigation. A short introduction to my research program can be found in my Research Statement.

Papers:
[With D. Rutherford] A combinatorial DGA for Legendrian knots from generating families (2011). arXiv.

Connections between Floer-type invariants and Morse-type invariants of Legendrian knots, Pacific Journal of Mathematics, 249-1 (2011), 77--133. Journal/arXiv.

Interests by 2000 Mathematics Subject Classification:
57M Low-dimensional topology
      57M25 Knots and links in S^3
      57M27 Invariants of knots and 3-manifolds
      57M50 Geometric structures on low-dimensional manifolds
57R17 Symplectic and contact topology
53D10 Contact manifolds, general

Maroon Bells Wilderness Area