Lenhard Lee Ng

Lenhard Ng
  • Eads Family Professor
External address: 216 Physics Bldg, 120 Science Drive, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-6972
Office Hours: 

Spring 2018:

  • Mondays 2:00-3:00
  • Thursdays 11:00-12:00

and by appointment.

Research Areas and Keywords

Geometry: Differential & Algebraic
symplectic geometry, contact geometry
Mathematical Physics
topological string theory
low-dimensional topology, knot theory

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.

Education & Training
  • Ph.D., Massachusetts Institute of Technology 2001

Selected Grants

Holomorphic Invariants in Symplectic Topology awarded by National Science Foundation (Principal Investigator). 2017 to 2020

Knots and contact topology through holomorphic curves awarded by National Science Foundation (Principal Investigator). 2014 to 2018

Simons Foundation Fellowship awarded by Simons Foundation (Principal Investigator). 2015 to 2016

CAREER: Symplectic Field Theory and Low-Dimensional Topology awarded by National Science Foundation (Principal Investigator). 2009 to 2015

Holomorphic Curves and Low-Dimensional Topology awarded by National Science Foundation (Principal Investigator). 2007 to 2010

Ekholm, T, Ng, L, and Shende, V. "A complete knot invariant from contact homology." Inventiones Mathematicae 211.3 (March 1, 2018): 1149-1200. Full Text Open Access Copy

Ng, L, Rutherford, D, Shende, V, and Sivek, S. "The cardinality of the augmentation category of a Legendrian link." MATHEMATICAL RESEARCH LETTERS 24.6 (2017): 1845-1874.

Cieliebak, K, Ekholm, T, Latschev, J, and Ng, L. "Knot contact homology, string topology, and the cord algebra." Journal de l'Ecole Polytechnique - Mathematiques 4 (January 1, 2017): 661-780. Full Text

Cornwell, C, Ng, L, and Sivek, S. "Obstructions to Lagrangian concordance." Algebraic & Geometric Topology 16.2 (April 26, 2016): 797-824. Full Text

Ekholm, T, and Ng, L. "Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold." Journal of Differential Geometry 101.1 (September 2015): 67-157. Full Text

Lipshitz, R, Ng, L, and Sarkar, S. "On transverse invariants from Khovanov homology." Quantum Topology 6.3 (January 1, 2015): 475-513. Full Text

Ng, L. "A topological introduction to knot contact homology." Bolyai Society Mathematical Studies 26 (January 1, 2014): 485-530. Full Text

Aganagic, M, Ekholm, T, Ng, L, and Vafa, C. "Topological strings, D-model, and knot contact homology." Advances in Theoretical and Mathematical Physics 18.4 (January 1, 2014): 827-956. Full Text

Ng, L, and Rutherford, D. "Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra." Algebraic and Geometric Topology 13.5 (2013): 3047-3097. Full Text

Ekholm, T, Etnyre, J, Ng, L, and Sullivan, M. "Filtrations on the knot contact homology of transverse knots." Mathematische Annalen 355.4 (2013): 1561-1591. Full Text


2016 PhD Graduates

Six graduate students participated in the May 15, 2016 graduation ceremonies to celebrate earning their PhDs in Mathematics. Their thesis topics were impressive and varied, and reflected the breadth of study in the department. Their advisors and... read more »

Lenhard Ng Wins Simons Award

In March 2015, it was announced by the Simons Foundation that Professor Lenhard (Lenny) Ng was awarded a Simons Fellowship for the 2015-2016 year (July 1, 2015 to June 30, 2016). He is among the 40 mathematicians in North America to earn the... read more »