Publications:
- On the Transverse Invariant for Bindings of Open Books
J. Differential Geom. 88 (2011), no. 3, 533-552. arXiv:0806.1729 [math.SG].
- Legendrian Contact Homology and Nondestabilizability
Joint with Clayton Shonkwiler: J. Symplectic Geom. 9 (2011), no. 1, 33-44 arXiv:0910.3914 [math.GT].
- Higher-Dimensional Linking Integrals
Joint with Clayton Shonkwiler: Proc. Amer. Math. Soc. 139 (2011), no. 4, 1511-1519 arXiv:0801.4022 [math.GT].
- Torsion and Open Book Decompositions
Joint with John B. Etnyre: Int. Math. Res. Not. (2010), no. 22, 4385-4398. arXiv:0909.3465 [math.SG].
- Triple Linking Numbers, Hopf Invariants and Integral Formulas for Three-Component Links
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin and Clayton Shonkwiler: Mat. Contemp. 34 (2008), 251-283. arXiv:0901.1612 [math.GT].
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The Four Vertex Theorem and its Converse
Joint with Dennis DeTurck, Herman Gluck and Daniel Pomerleano: Notices Amer. Math. Soc. 54 (2007), no. 2, 192-207 arXiv:0609268 [math.DG].
Preprints:
- On the Equivalence of Legendrian and Transverse Invariants in Knot Floer Homology
Joint with John A. Baldwin and Vera Vertesi: Submitted, 2011 arXiv:1112.5970 [math.SG].
- Generalized Gauss Maps and Integrals for Three-Component Links
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin and Clayton Shonkwiler: Submitted, 2011 arXiv:1101.3374 [math.GT].
In Preparation
- Bordered Sutured Floer Homology and Invariants of Legendrian Knots
Joint with John B. Etnyre and Rumen Zarev: ETA Spring 2012.
- Ruling Invariants and Augmentations of Bordered Legendrian Knots
Joint with Joshua Sabloff and Clayton Shonkwiler: ETA Spring 2012.
- Generalized Gauss Maps and Integrals for Three-Component Links: Part II
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Haggai Nuchi and Clayton Shonkwiler: ETA Spring 2012.
- Legendrian and Transverse Invariants in Heegaard Floer Homology: A Survey
Joint with John A. Baldwin: ETA Summer 2012.
- Contact Geometry and Heegaard Floer Invariant of Noncompact 3-manifolds
Joint with John B. Etnyre and Rumen Zarev: ETA Summer 2012.
- The Geometry of Triple Linking: A Survey
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Haggai Nuchi and Clayton Shonkwiler: ETA Summer 2012.
Talks:
On the Equivalence of Legendrian and transverse invariants in Heegaard Floer Homology (20 min.)- Spring 2012
Reconstructing HFK^- From Sutured Floer Homology (20 min.)- Spring 2011
Arnold's Dream: A Search for Higher-Order Helicity Invariants - Fall 2010
The Transverse Invariant and Bindings of Open Books (20 min.)- Fall 2008
The Four-Vertex Theorem and its Converse - Fall 2006
Khovanov Homology and the Slice Genus - Fall 2006
Taut to Tight: Foliations to Contact Structures - Summer 2006
A Few Facts About 3-manifolds (a cute little talk I gave on 3-manifolds) - Fall 2005
The Lickorish-Wallace Theorem - Fall 2005