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:

Office Location:	120 Science Drive, Durham, NC 27708
Email Address:
Web Page:	https://services.math.duke.edu/~ng/

Teaching (Spring 2025):

• MATH 612.01, ALGEBRAIC TOPOLOGY II Synopsis

  Physics 259, WF 01:25 PM-02:40 PM

Office Hours:

Fall 2024:

• Tuesdays 4:30-5:30 (Math 401; may end early)


• Wednesdays 2:30-3:30 (Math 401)


• Fridays 3:30-5:00 (Math 281S)

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)

• 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   (More Publications)

1. Feehan, PMN; Ng, LL; Ozsváth, PS, Frontiers in Geometry and Topology (July, 2024), pp. 320 pages, American Mathematical Society, ISBN 9781470470876  [abs]
2. Lipshitz, R; Ng, L, Torsion in linearized contact homology for Legendrian knots (August, 2023)  [abs]
3. 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]
4. 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]
5. Etnyre, JB; Ng, LL, Legendrian contact homology in $\mathbb{R}^3$, Surveys in Differential Geometry, vol. 25 no. 1 (2020), pp. 103-161, International Press of Boston [doi]

Recent Grant Support

• 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