Zion Canyon July 2019 with TEM.

Papers and Preprints

• ​Fillable contact structures from positive surgery (joint with T. Mark)

            Submitted, 2023

• On contact type hypersurfaces in 4-space   (joint with T. Mark)​​

             Inventiones Mathematicae, 228, 493-534, 2022.
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• Homology spheres bounding acyclic smooth manifolds and symplectic fillings.   (joint with J. Etnyre)

            Michigan Mathematical Journal, Advance Publication, 1-16,  DOI: 10.1307/mmj/20206003, 2022
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• Stein domains in C^2 with prescribed boundary.

            Advances in Geometry 22(1), 9-22, 2022.

• 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 CAREER award (DMS 2144363),  NSF Standard Award (DMS 2105525) and Simons Foundation Award (636841, BT).  ​