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 2020):
 MATH 620.01, SMOOTH MANIFOLDS
Synopsis
 Physics 205, MW 08:30 AM09:45 AM
 Office Hours:
 Tuesdays, 1:303:00 pm
Thursdays, 9:3011:00 am
 Education:
Ph.D.  Columbia University  2010 
A.B.  Harvard University  2005 
 Keywords:
Floer homology • Knot theory • Lowdimensional topology • Topology
 Recent Publications
(More Publications)
 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]
 Levine, AS; Lidman, T, SIMPLY CONNECTED, SPINELESS 4MANIFOLDS,
Forum of Mathematics, Sigma
(January, 2019) [doi] [abs]
 Levine, AS, Indivisible,
The Mathematical Intelligencer
(January, 2019) [doi]
 Levine, AS; Ruberman, D, Heegaard Floer invariants in codimension one,
Transactions of the American Mathematical Society
(2018),
pp. 11, American Mathematical Society (AMS) [doi]
 Recent Grant Support
 LowDimensional topology, Floer Homology, and Categorification, National Science Foundation, DMS1806437year 1, 2017/072021/04.
