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.

Please note: Lenhard has left the Mathematics department at Duke University; some info here might not be up to date.

Contact Info:

Office Location:	120 Science Drive, Durham, NC 27708
Office Phone:	(919) 660-6972
Email Address:
Web Page:	https://services.math.duke.edu/~ng/

Teaching (Fall 2023):

• MATH 401.01, INTRO ABSTRACT ALGEBRA Synopsis

  Physics 259, TuTh 03:05 PM-04:20 PM

• MATH 701.01, INTRO ABSTRACT ALGEBRA Synopsis

  Physics 259, TuTh 03:05 PM-04:20 PM

Office Hours:

Spring 2023:

• Mondays 1:00-2:30


• Thursdays 11:30-12:30

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. 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]
2. Ng, L; Rutherford, D; Shende, V; Sivek, S; Zaslow, E, Augmentations are Sheaves, Geometry and Topology, vol. 24 no. 5 (December, 2020), pp. 2149-2286, Mathematical Sciences Publishers [doi]  [abs]
3. Ekholm, T; Ng, L, Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials, Advances in Theoretical and Mathematical Physics, vol. 24 no. 8 (January, 2020), pp. 2067-2145 [doi]  [abs]
4. 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]
5. 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-Verlag [doi]  [abs]

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.      

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