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.
Office Location: | 120 Science Drive, Durham, NC 27708 |
Office Phone: | +1 919 660 2802 |
Email Address: | ![]() ![]() |
Web Page: | http://www.math.duke.edu/~alevine |
Ph.D. | Columbia University | 2010 |
A.B. | Harvard University | 2005 |