Zion Canyon July 2019 with TEM.

Papers and Preprints

• On contact type hypersurfaces in 4-space​​

           Joint with T. Mark. Submitted 2020

• Homology spheres bounding acyclic smooth manifolds and symplectic fillings.  

            Joint with J. Etnyre. Submitted, 2020
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• Stein domains in C^2 with prescribed boundary.

             To appear in Advances in Geometry.

• Mazur-type manifolds with L-space boundary 

            Joint with J. Conway. Math Research Letters, 27(1), 35-22, 2020.

• Tight small Seifert fibered spaces with e0=-2. 

            Algebraic and Geometric Topology, 20(1), 1-27, 2020.
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• Symplectic fillings, contact surgeries, and Lagrangian discs. 

            Joint with J. Conway and J. Etnyre.  International Mathematics Research Notices, rny291, 2019

• Obstructing pseudoconvex embeddings and contractible Stein fillings for Brieskorn spheres. 

            Joint with T. Mark. Advances in Mathematics 335, 878-895, 2018 

• Naturality of Heegaard Floer invariants under positive rational contact surgery 

            Joint with T. Mark. Journal of Differential Geometry, 110(2), 281-344, 2018 

• Hyperbolic rational homology spheres not admitting fillable contact structures.  

            Joint with A.Kaloti, Math Research Letters 24(6), 1693-1705, 2017. 

• On the Legendrian and transverse classification of cablings.

            Math Research Letters, 20(4), 787-803, 2013. 
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• Legendrian and transverse cables of positive torus knots,

            Joint with J. Etnyre and D. LaFountain, Geometry & Topology, 16, 1639-1689, 2012. 

Projects in progress

• Legendrian knots in overtwisted manifolds.

            Joint with P. Cahn

• Contact geometry of small Seifert FIbered Manifolds.

            Joint with J. Etnyre

• Non-thickenable embeddings of torus knots in lens spaces and its applications.

            Joint with J. Etnyre
 

Acknowledgement

 My research is supported by Simons Foundation Grant Award 636841, BT.