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:
Teaching (Fall 2023):
- MATH 790-90.05, MINICOURSE IN ADVANCED TOPICS
Synopsis
- Physics 227, TuTh 01:25 PM-02:40 PM
Teaching (Spring 2024):
- 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)
- 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]
- 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]
- 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]
- 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]
- 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.
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