Overview
My research mainly focuses on symplectic topology and low-dimensional topology. I am interested in studying structures in symplectic and contact geometry (Weinstein manifolds, contact manifolds, Legendrian and transverse knots), especially through holomorphic-curve techniques. One particular interest is extracting topological information about knots through cotangent bundles, and exploring relations to topological string theory. I have also worked in Heegaard Floer theory, quantum topology, and sheaf theory, especially as they relate to Legendrian and transverse knots.
Office Hours
Fall 2024:
- Tuesdays 4:30-5:30 (Math 401; may end early)
- Wednesdays 2:30-3:30 (Math 401)
- Fridays 3:30-5:00 (Math 281S)
Current Appointments & Affiliations
Professor of Mathematics
·
2016 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Frontiers in Geometry and Topology
Book · July 19, 2024 This volume contains the proceedings of the summer school and research conference “Frontiers in Geometry and Topology”, celebrating the sixtieth birthday of Tomasz Mrowka, which was held from August 1–12, 2022, at the Abdus Salam ... ... CiteAn L-infinity structure for Legendrian contact homology
Preprint · November 24, 2023 Link to item CiteTorsion in linearized contact homology for Legendrian knots
Journal Article · August 25, 2023 We present examples of Legendrian knots in $\mathbb{R}^3$ that have linearized Legendrian contact homology over $\mathbb{Z}$ containing torsion. As a consequence, we show that there exist augmentations of Legendrian knots over $\mathbb{Z}$ that are not ind ... Link to item CiteRecent Grants
Holomorphic Invariants of Knots and Contact Manifolds
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2020 - 2024Holomorphic Invariants in Symplectic Topology
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2017 - 2021Knots and contact topology through holomorphic curves
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2014 - 2018View All Grants
Education, Training & Certifications
Massachusetts Institute of Technology ·
2001
Ph.D.