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Lenhard L. Ng Curriculum Vitae

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Lenhard L. Ng Curriculum vitae Address Mathematics Department Telephone (919) 660-6972 Duke University, Box 90320 Fax (919) 660-2821 Durham, NC 27708-0320 WWW http://www.math.duke.edu/~ng/ E-mail ng[at]math.duke.edu Citizenship USA (born 1976, Stanford, CA) RESEARCH INTERESTS Low-dimensional topology, symplectic and contact geometry, differential geometry. Par- ticular interests: holomorphic curves, symplectic field theory, knot theory. CURRENT POSITION DUKE UNIVERSITY Associate Professor, Mathematics Department, 2011–present (Assistant Professor, 2006– 2011). EDUCATION MASSACHUSETTS INSTITUTE OF TECHNOLOGY (1996–2001) Ph.D. in mathematics, June 2001, Tomasz Mrowka, advisor. HARVARD UNIVERSITY (1993–1996) A.B. summa cum laude in mathematics and physics, June 1996. PAST EMPLOYMENT AND POSITIONS • Research Member, Mathematical Sciences Research Institute, spring 2010. • Visiting Assistant Professor, Princeton University, spring 2007. • American Institute of Mathematics Five-Year Fellow (postdoctoral), 2001–2006. • Lecturer in Mathematics and Visiting Scholar, Stanford University, 2002–2006. • Member, Institute for Advanced Study, 2001–2002. SELECTED AWARDS, GRANTS, AND HONORS • National Science Foundation: Principal Investigator on the following grants: • DMS-1406371 “Knots and Contact Topology Through Holomorphic Curves”, 2014– 2017; Lenhard L. Ng Curriculum vitae 2 • DMS-0846346 (CAREER) “Symplectic Field Theory and Low-Dimensional Topol- ogy”, 2009–2014; • DMS-0706777 “Holomorphic Curves and Low-Dimensional Topology”, 2007–2010. • Simons Foundation: Simons Fellow in Mathematics, 2015–2016. • American Institute of Mathematics: Five-Year Fellowship, 2001–2006. • Department of Defense: National Defense Science and Engineering Graduate (NDSEG) fellow, 1996–1999. • AMS/MAA/SIAM Frank and Brennie Morgan Prize for undergraduate research in mathematics: honorable mention (second place), 1996. • William Lowell Putnam Mathematical Competition: Putnam Fellow, 1993, 1994, 1995. • International Mathematical Olympiad: gold medal, 1992 (Moscow), 1993 (Istanbul); silver medal, 1991 (Sigtuna, Sweden). • USA Mathematical Olympiad: first place, 1992; winner, 1991, 1993. PUBLICATIONS (Papers are available at http://www.math.duke.edu/~ng/math/.) 1. Augmentations are sheaves (with D. Rutherford, V. Shende, S. Sivek, and E. Zaslow), preprint, arXiv:1502.04939. 2. Obstructions to Lagrangian concordance (with C. Cornwell and S. Sivek), submitted, arXiv:1411.1364. 3. Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold (with T. Ekholm), J. Differential Geom., to appear, arXiv:1307.8436. 4. Topological strings, D-model, and knot contact homology (with M. Aganagic, T. Ekholm, and C. Vafa), Adv. Theor. Math. Phys. 18 (2014), no. 4, 827–956. 5. On transverse invariants from Khovanov homology (with R. Lipshitz and S. Sarkar), Quantum Topol., to appear, arXiv:1303.6371. 6. A topological introduction to knot contact homology, in Contact and Symplectic Topol- ogy, Bolyai Soc. Math. Stud. 26 (Springer, Berlin, 2014). 7. Satellites of Legendrian knots and representations of the Chekanov–Eliashberg alge- bra (with D. Rutherford), Algebr. Geom. Topol. 13 (2013), no. 5, 3047–3097. 8. Knot contact homology (with T. Ekholm, J. Etnyre, and M. Sullivan), Geom. Topol. 17 (2013), 975–1112. 9. An atlas of Legendrian knots (with W. Chongchitmate), Exp. Math., 22 (2013), no. 1, 26–37. 10. Combinatorial knot contact homology and transverse knots, Adv. Math. 227 (2011), no. 6, 2189–2219. 11. Filtrations on the knot contact homology of transverse knots (with T. Ekholm, J. Etnyre, and M. Sullivan), Math. Annalen 355 (2013), no. 4, 1561–1591. 12. Legendrian and transverse twist knots (with J. Etnyre and V. Vertesi),´ J. Eur. Math. Soc. (JEMS) 15 (2013), no. 3, 451–512. Lenhard L. Ng Curriculum vitae 3 13. Grid diagrams, braids, and contact geometry (with D. Thurston), Proceedings of 15th G¨okovaGeometry–Topology Conference 2008, 120–136 (Gokova¨ Geometry–Topology Con- ference (GGT), Gokova,¨ 2009). 14. Rational Symplectic Field Theory for Legendrian knots, Invent. Math. 182 (2010), no. 3, 451–512. 15. A family of transversely nonsimple knots (with T. Khandhawit), Algebr. Geom. Topol. 10 (2010), no. 1, 293–314. 16. A skein approach to Bennequin type inequalities, Int. Math. Res. Not. 2008, Art. ID rnn116, 18 pp. 17. Transverse knots distinguished by knot Floer homology (with P.Ozsvath´ and D. Thurston), J. Symplectic Geom. 6 (2008), no. 4, 461–490. 18. On arc index and maximal Thurston–Bennequin number, J. Knot Theory Ramifications 21 (2012), no. 4, 1250031, 11 pp. 19. A Legendrian Thurston–Bennequin bound from Khovanov homology, Algebr. Geom. Topol. 5 (2005), 1637–1653. 20. The correspondence between augmentations and rulings for Legendrian knots (with J. Sabloff), Pacific J. Math. 224 (2006), no. 1, 141–150. 21. Plane curves and contact geometry, Proceedings of G¨okovaGeometry–Topology Conference 2005, 162–171 (Gokova¨ Geometry–Topology Conference (GGT), Gokova,¨ 2006). 22. Conormal bundles, contact homology, and knot invariants, in The interaction of finite type and Gromov–Witten invariants at the Banff International Research Station (2003), Geom. Topol. Monogr. 8 (2006), 129–144. 23. Framed knot contact homology, Duke Math. J. 141 (2008), no. 2, 365–406. 24. Legendrian solid-torus links (with L. Traynor), J. Symplectic Geom. 2 (2005), no. 3, 411– 443. 25. Knot and braid invariants from contact homology II, Geom. Topol. 9 (2005), 1603–1637. 26. Knot and braid invariants from contact homology I, Geom. Topol. 9 (2005), 247–297. 27. Problems in low dimensional contact geometry (with J. Etnyre), in Topology and Geom- etry of Manifolds, Proc. Sympos. Pure Math. 71 (2003), 337–357. 28. Invariants of Legendrian links and coherent orientations (with J. Etnyre and J. Sabloff), J. Symplectic Geom. 1 (2002), no. 2, 321–367. 29. Computable Legendrian invariants, Topology 42 (2003), no. 1, 55–82. 30. Maximal Thurston–Bennequin number of two-bridge links, Algebr. Geom. Topol. 1 (2001), 427–434. 31. The rook on the half-chessboard, or how not to diagonalize a matrix (with K. Kedlaya), Amer. Math. Monthly 105 (1998), no. 9, 819–824. 32. Hamiltonian decomposition of lexicographic products of digraphs, J. Combin. Theory Ser. B 73 (1998), no. 2, 119–129. 33. Hamiltonian decomposition of complete regular multipartite digraphs, Discrete Math. 177 (1997), no. 1-3, 279–285. 34. k-ordered hamiltonian graphs (with M. Schultz), J. Graph Theory 24 (1997), no. 1, 45–57. Lenhard L. Ng Curriculum vitae 4 SELECTED INVITED TALKS Lecture series, minicourses, and colloquia • Minicourse “Conormal bundles, knot invariants, and topological strings”, SwissMAP Geometry & Topology Conference, Engelberg, Switzerland, January 2015. • Colloquium, Princeton University, December 2014. • Minicourse “Grid diagrams and contact geometry”, Combinatorial Link Homology Theories, Braids, and Contact Geometry, ICERM, August 2014. • Colloquium, Northwestern University, May 2014. • Colloquium, University of California at Santa Barbara, November 2013. • Colloquium, Australian National University, June 2013. • Colloquium, University of Southern California, October 2012. • Invited Address “From holomorphic curves to knot invariants via the cotangent bun- dle”, American Mathematical Society Southeastern Section Meeting, Tulane University, October 2012. • Minicourse “Knot contact homology and applications”, Contact and Symplectic Topol- ogy Summer School and Conference, Alfred´ Renyi´ Institute of Mathematics, Budapest, July 2012. • Minicourse “Knots and the topology of three-manifolds”, conference “O Gosto pela Matematica”, Fundac¸ao Calouste Gulbenkian, Lisbon, July 2010. • Minicourse “Legendrian knots”, Introductory Workshop: Homology Theories of Knots and Links, Mathematical Sciences Research Institute, January 2010. • Minicourse “Contact geometry and three-dimensional topology”, Summer Graduate Workshop: Symplectic and Contact Geometry and Topology, Mathematical Sciences Research Institute, August 2009. • Minicourse “Legendrian Symplectic Field Theory”, Holomorphic Curves: Algebraic Structures and Geometric Application, Stanford University, August 2008. • Colloquium, Dartmouth College, May 2008. • Colloquium, University of North Carolina at Chapel Hill, November 2006. • Salomon Bochner Lectures in Mathematics, Rice University, October 2006. • Minicourse “Invariants of knots and links via SFT”, Workshop on Symplectic Field The- ory, Universitat¨ Leipzig, August 2006. • Colloquium, University of California at Berkeley, February 2006. • Colloquium, University of Illinois at Urbana–Champaign, January 2006. • Colloquium, University of Illinois at Chicago, January 2006. • Colloquium, Rutgers University, January 2006. • Colloquium, University of Toronto, January 2006. • Colloquium, University of Wisconsin, November 2005. • Colloquium, Columbia University, September 2005. • Minicourse, Courbes Holomorphes et Topologie de Contact, Summer school sponsored by CNRS, Berder, France, June 2003. Invited conference talks Lenhard L. Ng Curriculum vitae 5 • Quantum curves and quantum knot invariants, Banff International Resaerch Station, June 2014. • Low-dimensional topology after Floer, Universite´ de Montreal,´ July 2013. • Low dimensional topology, Simons Center for Geometry and Physics, Stony Brook, May 2013. • Southern California Topology Colloquium, Caltech, March 2013. • Interactions of gauge theory with contact and symplectic geometry in dimensions 3 and 4, Banff International Research Station, March 2013.
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