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Adam S. Levine

Associate Professor of Mathematics
Mathematics
120 Science Drive, Durham, NC 27708
Office hours Please email me for office hours.  

Research Interests


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, and Khovanov homology, which has its roots in representation theory. I am also interested in the interrelations between these invariants.

Selected Grants


Four-Manifolds and Categorification

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2022 - 2025

Low-Dimensional topology, Floer Homology, and Categorification

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2017 - 2022