Adam Simon Levine

Adam Simon Levine is an Associate Professor in the Department of Mathematics at Duke University, where he also serves as the Director of Undergraduate Studies for the mathematics department. His research focuses on the intricate structures of low-dimensional spaces and their applications to fundamental problems in topology.

Levine received his A.B. from Harvard University in 2005 and his Ph.D. from Columbia University in 2010. His academic journey has positioned him at the forefront of modern topological research, particularly in the study of 3- and 4-dimensional manifolds.

Levine's research interests center on low-dimensional topology, with particular emphasis on Heegaard Floer homology, Khovanov homology, and their applications to knot theory, concordance, and exotic 4-manifolds. His work explores how these powerful homological invariants reveal deep structures within seemingly simple geometric objects, particularly concerning the classification of smooth 4-dimensional manifolds—a problem that has challenged topologists for decades due to the unique complexities of four dimensions. He investigates connections between different invariants of knots in 3-space, especially the relationships between those arising from gauge theory, symplectic geometry, and representation theory.

Levine's recent publications demonstrate a consistent focus on advancing our understanding of knot concordance, slice knots, and the intricate relationships between different homology theories. His 2024 paper with Hedden provides a strengthened surgery formula for knot Floer homology, while his 2023 work on rationally slice knots reveals surprising uniformity across different constructions. The 2022 papers with Hom and Lidman, and with Gujral, respectively address fundamental questions about knot concordance in homology cobordisms and the behavior of Khovanov homology under cobordisms between split links.

Levine is actively involved in teaching and mentoring at Duke University. He has taught a wide range of courses from undergraduate linear algebra to advanced graduate topics in topology. In Fall 2025, he is scheduled to teach multiple sections of Linear Algebra. He has also led specialized minicourses on Knot Homologies, Link Homologies and Immersed Curves, and Introduction to 4-Manifolds, demonstrating his commitment to sharing cutting-edge research with students.

Levine's research is partially supported by an NSF grant titled 'Four-Manifolds and Categorification' (DMS-2203860), running from 2022-2026. His work has gained recognition beyond academia, with news coverage in the Duke Research Blog about his crossword puzzle contributions to the New York Times. In 2021, he was among the newly tenured faculty at Duke University, reflecting the high regard for his scholarly contributions.