Adam S. Levine, Associate Professor

My research is in low-dimensional topology, the study of the shapes of 3- and 4-dimensional spaces (manifolds) and of curves and surfaces contained therein. Classifying smooth 4-dimensional manifolds, in particular, has been a deep challenge for topologists for many decades; unlike in higher dimensions, there is not enough "wiggle room" to turn topological problems into purely algebraic ones. Many of my projects reveal new complications in the topology of 4-manifolds, particularly related to embedded surfaces. My main tools come from Heegaard Floer homology, a powerful package of invariants derived from symplectic geometry. I am also interested in the interrelations between different invariants of knots in 3-space, particularly the connections between knot invariants arising from gauge theory and symplectic geometry and those coming from representation theory.

Contact Info:

Office Location:	120 Science Drive, Durham, NC 27708
Office Phone:	(919) 660-2802
Email Address:
Web Page:	http://www.math.duke.edu/~alevine

Teaching (Fall 2023):

• MATH 790-90.05, MINICOURSE IN ADVANCED TOPICS Synopsis

  Physics 227, TuTh 01:25 PM-02:40 PM

• MATH 411.01, TOPOLOGY Synopsis

  Physics 119, TuTh 10:05 AM-11:20 AM

• MATH 711.01, TOPOLOGY Synopsis

  Physics 119, TuTh 10:05 AM-11:20 AM

Office Hours:

Please email me for office hours.

Education:

Ph.D.	Columbia University	2010
A.B.	Harvard University	2005

Keywords:

Floer homology • Knot theory • Low-dimensional topology • Topology

Recent Publications   (More Publications)

1. Hom, J; Levine, AS; Lidman, T, KNOT CONCORDANCE IN HOMOLOGY COBORDISMS, Duke Mathematical Journal, vol. 171 no. 15 (October, 2022), pp. 3089-3131 [doi]  [abs]
2. Gujral, OS; Levine, AS, Khovanov homology and cobordisms between split links, Journal of Topology, vol. 15 no. 3 (September, 2022), pp. 973-1016 [doi]  [abs]
3. Baldwin, JA; Dowlin, N; Levine, AS; Lidman, T; Sazdanovic, R, Khovanov homology detects the figure-eight knot, Bulletin of the London Mathematical Society, vol. 53 no. 3 (June, 2021), pp. 871-876 [doi]  [abs]
4. Celoria, D; Golla, M; Levine, AS, Heegaard floer homology and concordance bounds on the Thurston norm, Transactions of the American Mathematical Society, vol. 373 no. 1 (January, 2020), pp. 295-318 [doi]  [abs]
5. Levine, AS; Zemke, I, Khovanov homology and ribbon concordances, Bulletin of the London Mathematical Society, vol. 51 no. 6 (December, 2019), pp. 1099-1103 [doi]  [abs]

Recent Grant Support

• Four-Manifolds and Categorification, National Science Foundation, 2022/08-2025/07.      
• Low-Dimensional topology, Floer Homology, and Categorification, National Science Foundation, DMS-1806437-year 1, 2017/07-2022/04.