Skip to main content

Adam S. Levine

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

Overview


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.

Current Appointments & Affiliations


Associate Professor of Mathematics · 2020 - Present Mathematics, Trinity College of Arts & Sciences

In the News


Published October 25, 2021
Duke Math Professor Has NY Times Readers Tied Up in Knots With His Crossword Puzzle
Published October 21, 2021
Adam Simon Levine: Math's Breakout Crossword Puzzle Star
Published September 21, 2021
Meet the Newly Tenured Faculty of 2021

View All News

Recent Publications


A surgery formula for knot Floer homology

Journal Article Quantum Topology · January 1, 2024 Let K be a rationally null-homologous knot in a 3-manifold Y, equipped with a non-zero framing λ, and let Yλ(K) denote the result of λ-framed surgery on Y. Ozsváth and Szabó gave a formula for the Heegaard Floer homology groups of Yλ ... Full text Cite

A note on rationally slice knots

Journal Article New York Journal of Mathematics · January 1, 2023 Kawauchi proved that every strongly negative amphichiral knot (Formula Presented) bounds a smoothly embedded disk in some rational homology ball VK, whose construction a priori depends on K. We show that VK is inde-pendent of K up to ... Cite
View All Publications

Recent Grants


Four-Manifolds and Categorification

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2022 - 2026

Low-Dimensional topology, Floer Homology, and Categorification

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

View All Grants

Education, Training & Certifications


Columbia University · 2010 Ph.D.
Harvard University · 2005 A.B.