Lenhard Lee Ng | Scholars@Duke

Lenhard Lee 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.

Current Research Interests

Symplectic geometry, contact geometry, low-dimensional topology, knot theory, topological string theory.

Office Hours

Spring 2018:

Mondays 2:00-3:00
Thursdays 11:00-12:00

and by appointment.

Current Appointments & Affiliations

Eads Family Professor, Mathematics, Trinity College of Arts & Sciences 2016 - 2021
Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2016

Contact Information

216 Physics Bldg, 120 Science Drive, Durham, NC 27708
Box 90320, Durham, NC 27708-0320
ng@math.duke.edu (919) 660-6972
http://www.math.duke.edu/~ng/

Background
Education, Training, & Certifications
- Ph.D., Massachusetts Institute of Technology 2001
Duke Appointment History
- Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2011 - 2016
- Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2006 - 2011
Recognition
In the News
- APR 18, 2017
  
  Five Faculty Named Bass Fellows for Excellence in Teaching and Research
Awards & Honors
- Faculty Early Career Development (CAREER) Program. National Science Foundation. 2009
Expertise
Subject Headings
Research
Selected Grants
- Holomorphic Invariants in Symplectic Topology awarded by National Science Foundation 2017 - 2020
- Knots and contact topology through holomorphic curves awarded by National Science Foundation 2014 - 2018
- Simons Foundation Fellowship awarded by Simons Foundation 2015 - 2016
- CAREER: Symplectic Field Theory and Low-Dimensional Topology awarded by National Science Foundation 2009 - 2015
- Holomorphic Curves and Low-Dimensional Topology awarded by National Science Foundation 2007 - 2010
Publications & Artistic Works
Selected Publications
- Journal Articles
  - Ekholm, T, Ng, L, and Shende, V. "A complete knot invariant from contact homology." Inventiones Mathematicae 211, no. 3 (March 1, 2018): 1149-1200. Full Text Open Access Copy
  - Cieliebak, K, Ekholm, T, Latschev, J, and Ng, L. "Knot contact homology, string topology, and the cord algebra." Journal de l'Ecole Polytechnique - Mathematiques 4 (January 1, 2017): 661-780. Full Text
  - Ng, L, Rutherford, D, Shende, V, and Sivek, S. "The cardinality of the augmentation category of a Legendrian link." MATHEMATICAL RESEARCH LETTERS 24, no. 6 (2017): 1845-1874. Link to Item
  - Cornwell, C, Ng, L, and Sivek, S. "Obstructions to Lagrangian concordance." Algebraic & Geometric Topology 16, no. 2 (April 26, 2016): 797-824. Full Text
  - Ekholm, T, and Ng, L. "Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold." Journal of Differential Geometry 101, no. 1 (September 2015): 67-157. Full Text
  - Lipshitz, R, Ng, L, and Sarkar, S. "On transverse invariants from Khovanov homology." Quantum Topology 6, no. 3 (January 1, 2015): 475-513. Full Text
  - Aganagic, M, Ekholm, T, Ng, L, and Vafa, C. "Topological strings, D-model, and knot contact homology." Advances in Theoretical and Mathematical Physics 18, no. 4 (January 1, 2014): 827-956. Full Text
  - Ng, L. "A topological introduction to knot contact homology." Bolyai Society Mathematical Studies 26 (January 1, 2014): 485-530. Full Text
  - Ekholm, T, Etnyre, J, Ng, L, and Sullivan, M. "Filtrations on the knot contact homology of transverse knots." Mathematische Annalen 355, no. 4 (2013): 1561-1591. Full Text
  - Ekholm, T, Etnyre, JB, Ng, L, and Sullivan, MG. "Knot contact homology." Geometry and Topology 17, no. 2 (2013): 975-1112. Full Text
  - Ng, L, and Rutherford, D. "Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra." Algebraic and Geometric Topology 13, no. 5 (2013): 3047-3097. Full Text
  - Ekholm, T, Etnyre, J, Ng, L, and Sullivan, M. "Filtrations on the knot contact homology of transverse knots." Mathematische Annalen (2012): 1-31. Full Text
  - Ng, L. "On arc index and maximal Thurston-Bennequin number." Journal of Knot Theory and Its Ramifications 21, no. 4 (2012).
  - Chongchitmate, W, and Ng, L. "An atlas of Legendrian knots (Accepted)." Experimental Mathematics (2011). (Academic Article)
  - Etnyre, J, Ng, L, and Vertesi, V. "Legendrian and transverse twist knots (Accepted)." Journal of the European Mathematical Society (2011). (Academic Article)
  - Ng, L. "Combinatorial knot contact homology and transverse knots." Advances in Mathematics 227, no. 6 (2011): 2189-2219. Full Text
  - Khandhawit, T, and Ng, L. "A family of transversely nonsimple knots." Algebraic and Geometric Topology 10, no. 1 (2010): 293-314. Full Text
  - Ng, L. "Rational symplectic field theory for Legendrian knots." Inventiones Mathematicae 182, no. 3 (2010): 451-512. Full Text
  - Lenhard, NG. "A skein approach to bennequin-type inequalities." International Mathematics Research Notices 2008, no. 1 (2008). Full Text
  - Ng, L, Ozsvath, P, and Thurston, D. "Transverse knots distinguished by knot Floer homology." Journal of Symplectic Geometry 6, no. 4 (2008): 461-490. (Academic Article)
  - Ng, L. "Framed knot contact homology." Duke Mathematical Journal 141, no. 2 (2008): 365-406. Full Text
  - Muratori, MC, Stanley, JC, Ng, L, Ng, J, Gross, MUM, Tao, T, and Tao, B. "Insights from SMPY's greatest former child prodigies: Drs. Terence ("Terry") Tao and Lenhard ("Lenny") Ng reflect on their talent development." Gifted Child Quarterly 50, no. 4 (2006): 307-324.
  - NG, LL, and Sabloff, JM. "The correspondence between augmentations and rulings for legendrian knots." Pacific Journal of Mathematics 224, no. 1 (2006): 141-150. Full Text
  - Lenhard, NG, and Gadgil, S. "Knot and braid invariants from contact homology II." Geometry and Topology 9 (2005).
  - Ng, L, and Traynor, L. "Legendrian solid-torus links." Journal of Symplectic Geometry 2, no. 3 (2005): 411-443. (Academic Article)
  - Ng, L. "Knot and braid invariants from contact homology I." Geometry and Topology 9 (2005): 247-297. Full Text
  - Ng, L. "A Legendrian Thurston–Bennequin bound from Khovanov homology." Algebraic & Geometric Topology 5 (2005): 1637-1653. (Academic Article)
  - Ng, LL. "Computable Legendrian invariants." Topology 42, no. 1 (2003): 55-82. Full Text
  - Ng, L, Etnyre, J, and Sabloff, J. "Invariants of Legendrian links and coherent orientations." J. Symplectic Geom. 1, no. 2 (2002): 321-367. (Academic Article)
  - Ng, L. "Maximal Thurston–Bennequin number of two-bridge links." Algebr. Geom. Topol. 1 (2001): 427-434. (Academic Article)
  - Kedlaya, KS, and Ng, LL. "The rook on the half-chessboard, or how not to diagonalize a matrix." American Mathematical Monthly 105, no. 9 (1998): 819-824.
  - Ng, LL. "Hamiltonian Decomposition of Lexicographic Products of Digraphs." Journal of Combinatorial Theory. Series B 73, no. 2 (1998): 119-129. Full Text
  - Ng, L, and Schultz, M. "k-Ordered Hamiltonian Graphs." Journal of Graph Theory 24, no. 1 (1997): 45-57.
  - Ng, LL. "Hamiltonian decomposition of complete regular multipartite digraphs." Discrete Mathematics 177, no. 1-3 (1997): 279-285.
  - Ekholm, T, and Ng, L. "Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials." Link to Item
  - Ng, L, Rutherford, D, Shende, V, Sivek, S, and Zaslow, E. "Augmentations are Sheaves (Submitted)." Open Access Copy Link to Item
  - Ng, L, and Thurston, D. "Grid Diagrams, Braids, and Contact Geometry." Proceedings of Gokova Geometry-Topology Conference 2008, 120--136 . Link to Item
  - Ng, L. "Plane curves and contact geometry." Proceedings of G\~A{\P}kova Geometry-Topology Conference 2005 (2006), 165-174 . Link to Item
  - Ng, L. "Conormal bundles, contact homology and knot invariants." Geom. Topol. Monogr. 8: 129-144. Full Text Link to Item
  - Ng, LL. "The Legendrian satellite construction." Appears as part of"Legendrian solid-torus links", J. Symplectic Geom. 2 (2005), No. 3, 411-443 . Link to Item
  - Ng, LL. "Legendrian mirrors and Legendrian isotopy." Link to Item
Teaching & Mentoring
Recent Courses
- MATH 89S: First-Year Seminar 2018
- MATH 621: Differential Geometry 2018
- MATH 391: Independent Study 2017
- MATH 411: Topology 2017
- MATH 431: Advanced Calculus I 2017
- MATH 790-90: Minicourse in Advanced Topics 2017
Advising & Mentoring
- Current Ph.D. advisees:
  Chester Lian
  Orsola Capovilla-Searle
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Service to the Profession
Service to Duke

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Education, Training, & Certifications

Duke Appointment History

In the News

Awards & Honors

Subject Headings

Selected Grants

Selected Publications

Journal Articles

Recent Courses

Advising & Mentoring

Presentations & Appearances

Service to the Profession

Service to Duke