Adam S. Levine
- Assistant Professor of Mathematics
Research Areas and Keywords
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.
Levine, AS. "Computing knot Floer homology in cyclic branched covers." Algebraic & Geometric Topology 8.2 (July 25, 2008): 1163-1190. Full Text
Simon Levine, A, and Ruberman, D. "Heegaard Floer invariants in codimension one (Published online)." Transactions of the American Mathematical Society: 1-1. Full Text