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. Please note: Lenhard has left the Mathematics department at Duke University; some info here might not be up to date. - Contact Info:
Teaching (Fall 2023):
- MATH 401.01, INTRO ABSTRACT ALGEBRA
Synopsis
- Physics 259, TuTh 03:05 PM-04:20 PM
- MATH 701.01, INTRO ABSTRACT ALGEBRA
Synopsis
- Physics 259, TuTh 03:05 PM-04:20 PM
- Office Hours:
- Spring 2023:
- Mondays 1:00-2:30
- Thursdays 11:30-12:30
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)
- 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
(December, 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]
- Chantraine, B; Ng, L; Sivek, S, Representations, sheaves and Legendrian (2,m) torus links,
Journal of the London Mathematical Society, vol. 100 no. 1
(August, 2019),
pp. 41-82, WILEY [doi] [abs]
- Ekholm, T; Ng, L; Shende, V, A complete knot invariant from contact homology,
Inventiones Mathematicae, vol. 211 no. 3
(March, 2018),
pp. 1149-1200, Springer-Verlag [doi] [abs]
- Recent Grant Support
- Holomorphic Invariants of Knots and Contact Manifolds, National Science Foundation, 2020/09-2023/08.
- Holomorphic Invariants in Symplectic Topology, National Science Foundation, DMS-1707652, 2017/09-2021/08.
- 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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