Lenhard Lee Ng
- Professor of Mathematics
- Eads Family Professor
- Mondays 2:00-3:00
- Thursdays 11:00-12:00
and by appointment.
Research Areas and Keywords
Geometry: Differential & Algebraic
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.
Holomorphic Invariants in Symplectic Topology awarded by National Science Foundation (Principal Investigator). 2017 to 2020
Knots and contact topology through holomorphic curves awarded by National Science Foundation (Principal Investigator). 2014 to 2018
Simons Foundation Fellowship awarded by Simons Foundation (Principal Investigator). 2015 to 2016
CAREER: Symplectic Field Theory and Low-Dimensional Topology awarded by National Science Foundation (Principal Investigator). 2009 to 2015
Holomorphic Curves and Low-Dimensional Topology awarded by National Science Foundation (Principal Investigator). 2007 to 2010
Ekholm, T, Ng, L, and Shende, V. "A complete knot invariant from contact homology." Inventiones Mathematicae 211.3 (March 1, 2018): 1149-1200. Full Text Open Access Copy
Ng, L, Rutherford, D, Shende, V, and Sivek, S. "The cardinality of the augmentation category of a Legendrian link." MATHEMATICAL RESEARCH LETTERS 24.6 (2017): 1845-1874.
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
Ekholm, T, and Ng, L. "Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold." Journal of Differential Geometry 101.1 (September 2015): 67-157. Full Text
Lipshitz, R, Ng, L, and Sarkar, S. "On transverse invariants from Khovanov homology." Quantum Topology 6.3 (January 1, 2015): 475-513. Full Text
Ng, L. "A topological introduction to knot contact homology." Bolyai Society Mathematical Studies 26 (January 1, 2014): 485-530. 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 18.4 (January 1, 2014): 827-956. Full Text
Ekholm, T, Etnyre, J, Ng, L, and Sullivan, M. "Filtrations on the knot contact homology of transverse knots." Mathematische Annalen 355.4 (2013): 1561-1591. Full Text
Six graduate students participated in the May 15, 2016 graduation ceremonies to celebrate earning their PhDs in Mathematics. Their thesis topics were impressive and varied, and reflected the breadth of study in the department. Their advisors and... read more »