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:	216 Physics Bldg, 120 Science Drive, Durham, NC 27708
Office Phone:	(919) 660-6972
Email Address:
Web Page:	http://www.math.duke.edu/~ng/

Office Hours:

Fall 2019:

• Mondays 2:00-3:00


• Tuesdays 10:30-11:30

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)

• 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. 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]
2. 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 Nature [doi]  [abs]
3. Cieliebak, K; Ekholm, T; Latschev, J; Ng, L, Knot contact homology, string topology, and the cord algebra, Journal De L'Ecole Polytechnique Mathematiques, vol. 4 (January, 2017), pp. 661-780, Cellule MathDoc/CEDRAM [doi]  [abs]
4. 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, International Press of Boston [doi]
5. Cornwell, C; Ng, L; Sivek, S, Obstructions to Lagrangian concordance, Algebraic & Geometric Topology, vol. 16 no. 2 (April, 2016), pp. 797-824, Mathematical Sciences Publishers [arXiv:1411.1364], [doi]

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.      
• 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.      

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