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 Location: | 216 Physics Bldg, 120 Science Drive, Durham, NC 27708 |

Office Phone: | (919) 660-6972 |

Email Address: | |

Web Page: | http://www.math.duke.edu/~ng/ |

**Teaching (Spring 2018):**

- MATH 621.01,
*DIFFERENTIAL GEOMETRY*Synopsis- Physics 205, WF 03:05 PM-04:20 PM

**Office Hours:**- Spring 2018:
- Mondays 2:00-3:00
- Thursdays 11:00-12:00

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

**Current Ph.D. Students**- Yu Pan
- Caitlin Leverson

**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**- Ekholm, T; Ng, L; Shende, V,
*A complete knot invariant from contact homology*, Inventiones mathematicae, vol. 211 no. 3 (March, 2018), pp. 1149-1200 [doi] [abs] - Cieliebak, K; Ekholm, T; Latschev, J; Ng, L,
*Knot contact homology, string topology, and the cord algebra*, vol. 4 (January, 2017), pp. 661-780 [doi] [abs] - Ng, L; Rutherford, D; Shende, V; Sivek, S,
*The cardinality of the augmentation category of a Legendrian link*, Mathematical Research Letters, vol. 24 no. 6 (2017), pp. 1845-1874 - Cornwell, C; Ng, L; Sivek, S,
*Obstructions to Lagrangian concordance*, Algebraic and Geometric Topology, vol. 16 no. 2 (April, Accepted, 2016), pp. 797-824 [arXiv:1411.1364], [doi] - Ekholm, T; Ng, L,
*Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold*, Journal of Differential Geometry, vol. 101 no. 1 (September, 2015), pp. 67-157, ISSN 0022-040X [doi] [abs]

- Ekholm, T; Ng, L; Shende, V,

**Recent Grant Support***Holomorphic Invariants in Symplectic Topology*, National Science Foundation, DMS-1707652, 2017/09-2020/08.*Knots and contact topology through holomorphic curves*, National Science Foundation, DMS-1406371, 2014/09-2018/08.*Knots and contact topology through holomorphic curves*, National Science Foundation, DMS-1406371, 2014/09-2018/08.*Simons Foundation Fellowship*, Simons Foundation, 341289, 2015/07-2016/06.*CAREER: Symplectic Field Theory and Low-Dimensional Topology*, National Science Foundation, 0846346, 2009/09-2015/08.

**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