Adam S. Levine, Associate Professor
My research is in lowdimensional topology, the study of the shapes of 3 and 4dimensional spaces (manifolds) and of curves and surfaces contained therein. Classifying smooth 4dimensional 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 4manifolds, 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 3space, 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 79090.05, MINICOURSE IN ADVANCED TOPICS
Synopsis
 Physics 227, TuTh 01:25 PM02:40 PM
Teaching (Spring 2024):
 MATH 411.01, TOPOLOGY
Synopsis
 Physics 119, TuTh 10:05 AM11:20 AM
 MATH 711.01, TOPOLOGY
Synopsis
 Physics 119, TuTh 10:05 AM11:20 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 • Lowdimensional 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. 30893131 [doi] [abs]
 Gujral, OS; Levine, AS, Khovanov homology and cobordisms between split links,
Journal of Topology, vol. 15 no. 3
(September, 2022),
pp. 9731016 [doi] [abs]
 Baldwin, JA; Dowlin, N; Levine, AS; Lidman, T; Sazdanovic, R, Khovanov homology detects the figureeight knot,
Bulletin of the London Mathematical Society, vol. 53 no. 3
(June, 2021),
pp. 871876 [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. 295318 [doi] [abs]
 Levine, AS; Zemke, I, Khovanov homology and ribbon concordances,
Bulletin of the London Mathematical Society, vol. 51 no. 6
(December, 2019),
pp. 10991103 [doi] [abs]
 Recent Grant Support
 FourManifolds and Categorification, National Science Foundation, 2022/082025/07.
 LowDimensional topology, Floer Homology, and Categorification, National Science Foundation, DMS1806437year 1, 2017/072022/04.
