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
Office Phone:	(919) 660-6972
Email Address:
Web Page:	https://services.math.duke.edu/~ng/

Teaching (Fall 2021):

• MATH 611.01, ALGEBRAIC TOPOLOGY I Synopsis

  Physics 227, TuTh 12:00 PM-01:15 PM

• MATH 790-90.02, MINICOURSE IN ADVANCED TOPICS Synopsis

  Physics 205, MW 10:15 AM-11:30 AM

Office Hours:

Fall 2021, in person:

• Tuesdays 1:15-2:15 pm


• Wednesdays 1:00-2:00 pm

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. 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]
2. 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]
3. 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]
4. Edgar, GA; Ullman, DH; West, DB; Bracken, P; Brown, EA; Franco, Z; Friesen, C; Lipták, L; Luttmann, R; Miles, FB; Ng, L; Smiley, L; Stolarsky, K; Stong, R; Stromquist, W; Velleman, D; Wagon, S; Wilmer, E; Zeitz, P; Zhang, F, Problems and solutions, The American Mathematical Monthly, vol. 125 no. 1 (January, 2018), pp. 81-89 [doi]
5. Edgar, GA; Ullman, DH; West, DB; Bracken, P; Brown, EA; Franco, Z; Friesen, C; Lipták, L; Luttmann, R; Miles, FB; Ng, L; Smiley, L; Stolarsky, K; Stong, R; Stromquist, W; Velleman, D; Wagon, S; Wilmer, E; Zeitz, P; Zhang, F, Problems and solutions, The American Mathematical Monthly, vol. 124 no. 10 (December, 2017), pp. 970-978 [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.      

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