Lenhard L. Ng, Eads Family Professor
 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. - Contact Info:
Teaching (Fall 2025):
- MATH 611.01, ALGEBRAIC TOPOLOGY I
Synopsis
- Physics 205, TuTh 03:05 PM-04:20 PM
- Office Hours:
- Spring 2025:
- Mondays 1:00-2:00
- Wednesdays 2:45-3:45 (may end early)
and by appointment.
- Education:
Ph.D. | Massachusetts Institute of Technology | 2001 |
AB | Harvard University | 1996 |
- Specialties:
-
Geometry
Topology
- Research Interests: Symplectic geometry, Low dimensional topology, Contact geometry, Knot theory, Holomorphic curves
- Keywords:
- Contact geometry • Holomorphic curves • Knot theory • Low dimensional topology • Symplectic and contact topology • Symplectic geometry • Three-manifolds (Topology) • Topology
- Curriculum Vitae
- Current Ph.D. Students
(Former Students)
- Postdocs Mentored
- Christopher Cornwell (2011 - 2014)
- Daniel Rutherford (2008 - 2011)
- Undergraduate Research Supervised
- Alexandru Milu (2014 - 2015)
- Alexandru Milu (May 12, 2014 - June 27, 2014)
- Wutichai Chongchitmate (2009 - 2010)
- Tirasan Khandhawit (2007 - 2008)
- Recent Publications
(More Publications)
- Feehan, PMN; Ng, LL; Ozsváth, PS, Frontiers in Geometry and Topology
(July, 2024),
pp. 320 pages, American Mathematical Society, ISBN 9781470470876 [abs]
- Lipshitz, R; Ng, L, Torsion in linearized contact homology for Legendrian knots
(August, 2023) [abs]
- Casals, R; Ng, L, Braid loops with infinite monodromy on the Legendrian contact DGA,
Journal of Topology, vol. 15 no. 4
(December, 2022),
pp. 1927-2016, WILEY [doi] [abs]
- Ng, L; Rutherford, D; Shende, V; Sivek, S; Zaslow, E, Augmentations are sheaves,
Geometry and Topology, vol. 24 no. 5
(January, 2020),
pp. 2149-2286, Mathematical Sciences Publishers [doi] [abs]
- Ekholm, T; Ng, L, Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials,
Advances in Theoretical and Mathematical Physics, vol. 24 no. 8
(January, 2020),
pp. 2067-2145 [doi] [abs]
- Recent Grant Support
- Enhanced invariants of Legendrian links, National Science Foundation, 2025/07-2028/06.
- Holomorphic Invariants of Knots and Contact Manifolds, National Science Foundation, 2020/09-2024/08.
- Conferences Organized
- Organizer : 27th Annual Geometry Festival. April 27, 2012 - April 29, 2012, Organizer : 27th Annual Geometry Festival, April 27, 2012 - April 29, 2012
- Organizer, workshop "Cyclic homology and symplectic topology". November, 2009, Organizer, workshop "Cyclic homology and symplectic topology", November, 2009
- Organizer, workshop "Algebraic structures in the theory of holomorphic curves". November, 2009, Organizer, workshop "Algebraic structures in the theory of holomorphic curves", November, 2009
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