Adam S. Levine, Assistant Professor

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.

Contact Info:

Office Location:	120 Science Drive, 211 Physics Building, Durham, NC 27708
Office Phone:	(919) 660-2802
Email Address:
Web Page:	http://www.math.duke.edu/~alevine

Office Hours:

Tuesdays, 1:30-3:00 pm
Thursdays, 9:30-11:00 am

Education:

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

Keywords:

Floer homology • Knot theory • Low-dimensional topology • Topology

Recent Publications   (More Publications)

1. Levine, AS; Lidman, T, SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS, Forum of Mathematics, Sigma (January, 2019) [doi]  [abs]
2. Levine, AS; Ruberman, D, Heegaard Floer invariants in codimension one, Transactions of the American Mathematical Society (2018), pp. 1-1, American Mathematical Society (AMS) [doi]
3. Baldwin, JA; Levine, AS; Sarkar, S, Khovanov homology and knot Floer homology for pointed links, Journal of Knot Theory and Its Ramifications, vol. 26 no. 02 (February, 2017), pp. 1740004-1740004, World Scientific Pub Co Pte Lt [doi]
4. Greene, J; Levine, A, Strong Heegaard diagrams and strong L–spaces, Algebraic & Geometric Topology, vol. 16 no. 6 (December, 2016), pp. 3167-3208, Mathematical Sciences Publishers [doi]
5. Hedden, M; Levine, AS, Splicing knot complements and bordered Floer homology, Journal Fur Die Reine Und Angewandte Mathematik, vol. 2016 no. 720 (January, 2016), WALTER DE GRUYTER GMBH [doi]  [abs]

Recent Grant Support

• Low-Dimensional topology, Floer Homology, and Categorification, National Science Foundation, DMS-1806437-year 1, 2017/07-2020/04.