# Lenhard Lee Ng

- Eads Family Professor
- Professor of Mathematics

**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:**

Fall 2019:

- Mondays 2:00-3:00
- Tuesdays 10:30-11:30

and by appointment.

### Research Areas and Keywords

##### Geometry: Differential & Algebraic

symplectic geometry, contact geometry

##### Mathematical Physics

topological string theory

##### Topology

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.

### 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

Chantraine, Baptiste, et al. “Representations, sheaves and Legendrian (2,m) torus links.” *Journal of the London Mathematical Society Second Series*, vol. 100, no. 1, WILEY, Aug. 2019, pp. 41–82. *Wos*, doi:10.1112/jlms.12204.
Full Text Open Access Copy

Ekholm, T., et al. “A complete knot invariant from contact homology.” *Inventiones Mathematicae*, vol. 211, no. 3, Mar. 2018, pp. 1149–200. *Scopus*, doi:10.1007/s00222-017-0761-1.
Full Text Open Access Copy

Ng, Lenhard, et al. “The cardinality of the augmentation category of a Legendrian link.” *Mathematical Research Letters*, vol. 24, no. 6, 2017, pp. 1845–74.
Open Access Copy

Cieliebak, K., et al. “Knot contact homology, string topology, and the cord algebra.” *Journal De L’Ecole Polytechnique Mathematiques*, vol. 4, Jan. 2017, pp. 661–780. *Scopus*, doi:10.5802/jep.55.
Full Text Open Access Copy

Cornwell, Christopher, et al. “Obstructions to Lagrangian concordance.” *Algebraic & Geometric Topology*, vol. 16, no. 2, Mathematical Sciences Publishers, Apr. 2016, pp. 797–824. *Crossref*, doi:10.2140/agt.2016.16.797.
Full Text Open Access Copy

Ekholm, T., and L. Ng. “Legendrian contact homology in the boundary of a subcritical weinstein 4-Manifold.” *Journal of Differential Geometry*, vol. 101, no. 1, Sept. 2015, pp. 67–157. *Scopus*, doi:10.4310/jdg/1433975484.
Full Text Open Access Copy

Lipshitz, R., et al. “On transverse invariants from Khovanov homology.” *Quantum Topology*, vol. 6, no. 3, Jan. 2015, pp. 475–513. *Scopus*, doi:10.4171/QT/69.
Full Text Open Access Copy

Aganagic, M., et al. “Topological strings, D-model, and knot contact homology.” *Advances in Theoretical and Mathematical Physics*, vol. 18, no. 4, Jan. 2014, pp. 827–956. *Scopus*, doi:10.4310/ATMP.2014.v18.n4.a3.
Full Text Open Access Copy

Ng, L. “A topological introduction to knot contact homology.” *Bolyai Society Mathematical Studies*, vol. 26, Jan. 2014, pp. 485–530. *Scopus*, doi:10.1007/978-3-319-02036-5_10.
Full Text Open Access Copy

Ng, L., and D. Rutherford. “Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra.” *Algebraic and Geometric Topology*, vol. 13, no. 5, Aug. 2013, pp. 3047–97. *Scopus*, doi:10.2140/agt.2013.13.3047.
Full Text Open Access Copy

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Professor Lenny Ng has been elected to the American Mathematical Society for his contributions to Floer homology and low-dimensional topology and service to the mathematical community. The Fellows of the American Mathematical Society program... read more »

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 »

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 »