Zion Canyon July 2019 with TEM.

Papers and Preprints

• On contact type hypersurfaces in 4-space​​

           Joint with T. Mark. To appear in Inventiones Mathematicae.

• Homology spheres bounding acyclic smooth manifolds and symplectic fillings.  

            Joint with J. Etnyre. To appear in Michigan Mathematical Journal.
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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), 35-42, 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, 2021(8), 6020-6050, 2021

• 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 an NSF Award (DMS 2105525) and Simons Foundation Grant Award (636841, BT).  ​