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 2021, on Zoom:

Tuesdays 9:45-10:45 am
Wednesdays 1:00-2:00 pm

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

120 Science Drive, Durham, NC 27708
216 Physics Building, Box 90320, Durham, NC 27708-0320
ng@math.duke.edu (919) 660-6972
https://services.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
Leadership & Clinical Positions at Duke
- Director of Undergraduate Research and Prizes. Duke Mathematics Department, 2019 to present.
Recognition
In the News
- NOV 8, 2018 Duke Today
  
  Duke Professor Named Fellow of the American Mathematical Society
- APR 18, 2017
  
  Five Faculty Named Bass Fellows for Excellence in Teaching and Research
Awards & Honors
Expertise
Subject Headings
Research
Selected Grants
- Holomorphic Invariants of Knots and Contact Manifolds awarded by National Science Foundation 2020 - 2023
- Holomorphic Invariants in Symplectic Topology awarded by National Science Foundation 2017 - 2021
- 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
- Academic Articles
  - Chantraine, Baptiste, Lenhard Ng, and Steven Sivek. “Representations, sheaves and Legendrian (2,m) torus links.” Journal of the London Mathematical Society Second Series 100, no. 1 (August 1, 2019): 41–82. https://doi.org/10.1112/jlms.12204.
    Full Text Open Access Copy Link to Item
  - Ekholm, T., L. Ng, and V. Shende. “A complete knot invariant from contact homology.” Inventiones Mathematicae 211, no. 3 (March 1, 2018): 1149–1200. https://doi.org/10.1007/s00222-017-0761-1.
    Full Text Open Access Copy
  - Edgar, G. A., D. H. Ullman, D. B. West, P. Bracken, E. A. Brown, Z. Franco, C. Friesen, et al. “Problems and solutions.” American Mathematical Monthly 125, no. 1 (January 1, 2018): 81–89. https://doi.org/10.1080/00029890.2018.1397465.
    Full Text
  - Edgar, G. A., D. H. Ullman, D. B. West, P. Bracken, E. A. Brown, Z. Franco, C. Friesen, et al. “Problems and solutions.” American Mathematical Monthly 124, no. 10 (December 1, 2017): 970–78. https://doi.org/10.4169/amer.math.monthly.124.10.970.
    Full Text
  - Edgar, G. A., D. H. Ullman, D. B. West, P. Bracken, E. A. Brown, Z. Franco, C. Friesen, et al. “Problems and solutions.” American Mathematical Monthly 124, no. 8 (October 1, 2017): 754–62. https://doi.org/10.4169/amer.math.monthly.124.8.754.
    Full Text
  - Edgar, G. A., D. H. Ullman, D. B. West, P. Bracken, E. A. Brown, Z. Franco, C. Friesen, et al. “Problems and solutions.” American Mathematical Monthly 124, no. 5 (May 1, 2017): 465–74. https://doi.org/10.4169/amer.math.monthly.124.5.465.
    Full Text
  - Cieliebak, K., T. Ekholm, J. Latschev, and L. Ng. “Knot contact homology, string topology, and the cord algebra.” Journal De L’Ecole Polytechnique Mathematiques 4 (January 1, 2017): 661–780. https://doi.org/10.5802/jep.55.
    Full Text Open Access Copy
  - Ng, Lenhard, Dan Rutherford, Vivek Shende, and Steven Sivek. “The cardinality of the augmentation category of a Legendrian link.” Mathematical Research Letters 24, no. 6 (2017): 1845–74.
    Open Access Copy Link to Item
  - Cornwell, Christopher, Lenhard Ng, and Steven Sivek. “Obstructions to Lagrangian concordance.” Algebraic & Geometric Topology 16, no. 2 (April 26, 2016): 797–824. https://doi.org/10.2140/agt.2016.16.797.
    Full Text Open Access Copy
  - Ekholm, T., and L. Ng. “Legendrian contact homology in the boundary of a subcritical weinstein 4-Manifold.” Journal of Differential Geometry 101, no. 1 (September 1, 2015): 67–157. https://doi.org/10.4310/jdg/1433975484.
    Full Text Open Access Copy
  - Lipshitz, R., L. Ng, and S. Sarkar. “On transverse invariants from Khovanov homology.” Quantum Topology 6, no. 3 (January 1, 2015): 475–513. https://doi.org/10.4171/QT/69.
    Full Text Open Access Copy
  - Aganagic, M., T. Ekholm, L. Ng, and C. Vafa. “Topological strings, D-model, and knot contact homology.” Advances in Theoretical and Mathematical Physics 18, no. 4 (January 1, 2014): 827–956. https://doi.org/10.4310/ATMP.2014.v18.n4.a3.
    Full Text Open Access Copy
  - Ng, L. “A topological introduction to knot contact homology.” Bolyai Society Mathematical Studies 26 (January 1, 2014): 485–530. https://doi.org/10.1007/978-3-319-02036-5_10.
    Full Text Open Access Copy
  - Ng, L., and D. Rutherford. “Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra.” Algebraic and Geometric Topology 13, no. 5 (August 1, 2013): 3047–97. https://doi.org/10.2140/agt.2013.13.3047.
    Full Text Open Access Copy
  - Ekholm, T., J. B. Etnyre, L. Ng, and M. G. Sullivan. “Knot contact homology.” Geometry and Topology 17, no. 2 (May 13, 2013): 975–1112. https://doi.org/10.2140/gt.2013.17.975.
    Full Text Open Access Copy
  - Etnyre, J. B., L. L. Ng, and V. Vertesi. “Legendrian and transverse twist knots.” Journal of the European Mathematical Society 15, no. 3 (May 13, 2013): 969–95. https://doi.org/10.4171/JEMS/383.
    Full Text
  - Ekholm, T., J. Etnyre, L. Ng, and M. Sullivan. “Filtrations on the knot contact homology of transverse knots.” Mathematische Annalen 355, no. 4 (April 1, 2013): 1561–91. https://doi.org/10.1007/s00208-012-0832-y.
    Full Text
  - Chongchitmate, W., and L. Ng. “An atlas of Legendrian knots.” Experimental Mathematics 22, no. 1 (January 1, 2013): 26–37. https://doi.org/10.1080/10586458.2013.750221.
    Full Text
  - Ng, L. “On arc index and maximal Thurston-Bennequin number.” Journal of Knot Theory and Its Ramifications 21, no. 4 (2012).
    Open Access Copy
  - Ng, L. “Combinatorial knot contact homology and transverse knots.” Advances in Mathematics 227, no. 6 (August 20, 2011): 2189–2219. https://doi.org/10.1016/j.aim.2011.04.014.
    Full Text
  - Ng, L. “Rational symplectic field theory for Legendrian knots.” Inventiones Mathematicae 182, no. 3 (December 1, 2010): 451–512. https://doi.org/10.1007/s00222-010-0265-8.
    Full Text
  - Khandhawit, T., and L. Ng. “A family of transversely nonsimple knots.” Algebraic and Geometric Topology 10, no. 1 (July 28, 2010): 293–314. https://doi.org/10.2140/agt.2010.10.293.
    Full Text
  - Lenhard, N. G. “A skein approach to bennequin-type inequalities.” International Mathematics Research Notices 2008, no. 1 (December 1, 2008). https://doi.org/10.1093/imrn/rnn116.
    Full Text
  - Ng, L. “Framed knot contact homology.” Duke Mathematical Journal 141, no. 2 (February 1, 2008): 365–406. https://doi.org/10.1215/S0012-7094-08-14125-0.
    Full Text
  - Ng, Lenhard, Peter Ozsváth, and Dylan Thurston. “Transverse knots distinguished by knot Floer homology.” Journal of Symplectic Geometry 6, no. 4 (2008): 461–90. https://doi.org/10.4310/jsg.2008.v6.n4.a4.
    Full Text
  - Ng, Lenhard. “Conormal bundles, contact homology and knot invariants.” The Interaction of Finite Type and Gromov Witten (Birs 2003), April 22, 2006. https://doi.org/10.2140/gtm.2006.8.129.
    Full Text
  - NG, L. L., and J. M. Sabloff. “The correspondence between augmentations and rulings for legendrian knots.” Pacific Journal of Mathematics 224, no. 1 (March 1, 2006): 141–50. https://doi.org/10.2140/pjm.2006.224.141.
    Full Text
  - Muratori, M. C., J. C. Stanley, L. Ng, J. Ng, M. U. M. Gross, T. Tao, and B. Tao. “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 (January 1, 2006): 307–24. https://doi.org/10.1177/001698620605000404.
    Full Text
  - Ng, Lenhard. “A Legendrian Thurston–Bennequin bound from Khovanov homology.” Algebraic & Geometric Topology 5, no. 4 (November 25, 2005): 1637–53. https://doi.org/10.2140/agt.2005.5.1637.
    Full Text
  - Lenhard, N. G., and S. Gadgil. “Knot and braid invariants from contact homology II.” Geometry and Topology 9 (August 26, 2005).
  - Ng, L. “Knot and braid invariants from contact homology I.” Geometry and Topology 9 (January 26, 2005): 247–97. https://doi.org/10.2140/gt.2005.9.247.
    Full Text
  - Ng, L., and L. Traynor. “Legendrian solid-torus links.” Journal of Symplectic Geometry 2, no. 3 (2005): 411–43.
  - Ng, L. L. “Computable Legendrian invariants.” Topology 42, no. 1 (January 1, 2003): 55–82. https://doi.org/10.1016/S0040-9383(02)00010-1.
    Full Text
  - Ng, L., J. Etnyre, and J. Sabloff. “Invariants of Legendrian links and coherent orientations.” J. Symplectic Geom. 1, no. 2 (2002): 321–67.
  - Ng, Lenhard. “Maximal Thurston–Bennequin number of two-bridge links.” Algebraic & Geometric Topology 1, no. 1 (July 31, 2001): 427–34. https://doi.org/10.2140/agt.2001.1.427.
    Full Text
  - Ng, L. L. “Hamiltonian Decomposition of Lexicographic Products of Digraphs.” Journal of Combinatorial Theory. Series B 73, no. 2 (July 1, 1998): 119–29. https://doi.org/10.1006/jctb.1998.1816.
    Full Text
  - Kedlaya, K. S., and L. L. Ng. “The rook on the half-chessboard, or how not to diagonalize a matrix.” American Mathematical Monthly 105, no. 9 (January 1, 1998): 819–24. https://doi.org/10.2307/2589210.
    Full Text
  - Ng, L. L. “Hamiltonian decomposition of complete regular multipartite digraphs.” Discrete Mathematics 177, no. 1–3 (December 1, 1997): 279–85. https://doi.org/10.1016/S0012-365X(97)00017-4.
    Full Text
  - Ng, L., and M. Schultz. “k-Ordered Hamiltonian Graphs.” Journal of Graph Theory 24, no. 1 (January 1, 1997): 45–57. https://doi.org/10.1002/(SICI)1097-0118(199701)24:1<45::AID-JGT6>3.0.CO;2-J.
    Full Text
  - Casals, Roger, and Lenhard Ng. “Braid Loops with infinite monodromy on the Legendrian contact DGA,” n.d.
    Link to Item
  - Ekholm, Tobias, and Lenhard Ng. “Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials (Submitted),” n.d.
    Open Access Copy Link to Item
  - Etnyre, John B., and Lenhard L. Ng. “Legendrian contact homology in R^3 (Submitted),” n.d.
    Open Access Copy Link to Item
  - Ng, L., D. Rutherford, V. Shende, S. Sivek, and E. Zaslow. “Augmentations are Sheaves (Accepted).” Geometry and Topology, n.d.
    Open Access Copy Link to Item
  - Ng, Lenhard L. “The Legendrian satellite construction.” Appears as Part Of"Legendrian Solid Torus Links", J. Symplectic Geom. 2 (2005), No. 3, 411 443, n.d.
    Link to Item
  - Ng, Lenhard L. “Legendrian mirrors and Legendrian isotopy,” n.d.
    Link to Item
  - Ng, Lenhard, and Dylan Thurston. “Grid Diagrams, Braids, and Contact Geometry.” Proceedings of Gokova Geometry Topology Conference 2008, 120 136, n.d.
    Link to Item
  - Ng, Lenhard. “Plane curves and contact geometry.” Proceedings of G\~A{\P}Kova Geometry Topology Conference 2005 (2006), 165 174, n.d.
    Link to Item
Teaching & Mentoring
Recent Courses
- MATH 611: Algebraic Topology I 2021
- MATH 633: Complex Analysis 2021
- MATH 112L: Laboratory Calculus II 2020
- MATH 411: Topology 2020
- MATH 491: Independent Study 2020
- MATH 494: Research Independent Study 2020
- MATH 711: Topology 2020
- MATH 790-90: Minicourse in Advanced Topics 2020
- MATH 112L: Laboratory Calculus II 2019
- MATH 393: Research Independent Study 2019
- MATH 493: Research Independent Study 2019
- MATH 611: Algebraic Topology I 2019
- MATH 612: Algebraic Topology II 2019
Advising & Mentoring
- Current Ph.D. advisees:
  Orsola Capovilla-Searle
  Chindu Mohanakumar
  
  Current postdoctoral fellows mentored:
  Ziva Myer, Elliot Assistant Research Professor
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Service to the Profession
Service to Duke

Some information on this profile has been compiled automatically from Duke databases and external sources. (Our About page explains how this works.) If you see a problem with the information, please write to Scholars@Duke and let us know. We will reply promptly.

Education, Training, & Certifications

Duke Appointment History

Leadership & Clinical Positions at Duke

In the News

Awards & Honors

Subject Headings

Selected Grants

Selected Publications

Academic Articles

Recent Courses

Advising & Mentoring

Presentations & Appearances

Service to the Profession

Service to Duke