Research

Publications:

Lifting Lagrangian immersions in CP^(n-1) to Lagrangian cones in C^n
Joint with Scott Baldridge and Ben McCarty.
Submitted, 2017
arXiv: 1708.09048 [math.GT]

Transverse braids and combinatorial knot Floer homology
Joint with Peter Lambert-Cole:
Submitted, 2017
arXiv: 1703.06861 [math.SG]

LSVBraids and combinatorial knot Floer homology
Joint with Peter Lambert-Cole and Michaela Stone:
Under revision at Mathematical Research Letters, 2016
arXiv: 1312.5586 [math.GT]

Bypass Exact Triangle

Sutured Floer homology and invariants of Legendrian and transverse knots
Joint with John B. Etnyre and Rumen Zarev:
Geometry & Topology 21 (2017), no. 2, 1469-1582 (journal link)
doi: 10.2140/gt.2017.21.1469; arXiv: 1408.5858 [math.GT]

Stereographic

Generalized Gauss Maps and Integrals for Three-Component Links: Toward Higher Helicities for Magnetic Fields and Fluid Flows, Part 2
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Haggai Nuchi and Clayton Shonkwiler:
Algebraic & Geometric Topology 13 (2013), no. 5, 2897-2923 (journal link)
MR: 3116307; Zbl: 06198033; doi: 10.2140/agt.2013.13.2897; arXiv: 1207.1793 [math.GT]

BraidDiagram - 1

On the Equivalence of Legendrian and Transverse Invariants in Knot Floer Homology
Joint with John A. Baldwin and Vera Vertesi:
Geometry & Topology 17 (2013), no. 2, 925-974 (journal link)
MR: 3070518; Zbl: 1285.57005; doi: 10.2140/gt.2013.17.925; arXiv: 1112.5970 [math.SG]


G2R4
Generalized Gauss Maps and Integrals for Three-Component Links: Toward Higher Helicities for Magnetic Fields and Fluid Flows
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin and Clayton Shonkwiler:
Journal of Mathematical Physics 54 013515 (2013) (journal link)
MR: 3059903; Zbl: 06255553; doi: 10.1063/1.4774172; arXiv: 1101.3374 [math.GT]

Stabilize

On the Transverse Invariant for Bindings of Open Books
Journal of Differential Geometry 88 (2011), no. 3, 533-552
MR: 2844442; Zbl: 06011497; arXiv: 0806.1729 [math.SG]

 

LCH - 1

Legendrian Contact Homology and Nondestabilizability
Joint with Clayton Shonkwiler:
Journal of Symplectic Geometry 9 (2011), no. 1, 33-44 (journal link)
MR: 2787360; Zbl: 1226.57013; doi: 10.4310/JSG.2011.v9.n1.a3; arXiv: 0910.3914 [math.GT]


HigherDimLinking - 1
Higher-Dimensional Linking Integrals
Joint with Clayton Shonkwiler:
Proceedings of the American Mathematical Society 139 (2011), no. 4, 1511-1519 (journal link)
MR: 2748445; Zbl: 1221.57038; doi: 10.1090/S0002–9939–2010–10603–2; arXiv: 0801.4022 [math.GT]

 

Bindings - 1

Torsion and Open Book Decompositions
Joint with John B. Etnyre:
International Mathematics Research Notices (2010), no. 22, 4385-4398
MR: 2737776; Zbl: 1213.57028; doi: 10.1093.imrn.rnq054; arXiv: 0909.3465 [math.SG].

 

TL1 - 1

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:
Matemátcia Contemporânea 34 (2008), 251-283 (journal link)
Special volume in honor of Manfredo P. do Carmo’s 80th birthday.
MR: 2588614; Zbl: 1194.57007; arXiv: 0901.1612 [math.GT]

Four Vertex Theorem

The Four Vertex Theorem and its Converse
Joint with Dennis DeTurck, Herman Gluck and Daniel Pomerleano:
Notices of the American Mathematical Society 54 (2007), no. 2, 192-207 (journal link)
MR: 2285124; arXiv: 0609268 [math.DG]

 


In Preparation:

  • A refinement of the Heegaard Floer contact invariant
    Joint with John A. Baldwin.
  • Contact Geometry and Heegaard Floer Invariant of Noncompact 3-manifolds
    Joint with John B. Etnyre.
  • Ruling Invariants and Augmentations of Bordered Legendrian Knots
    Joint with Joshua Sablof and Clayton Shonkwiler.
  • Legendrian and Transverse Invariants in Heegaard Floer Homology: A Survey
    Joint with John A. Baldwin.
  • The Geometry of Triple Linking: A Survey
    Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Haggai Nuchi and Clayton Shonkwiler.

Talks: