Adam S. Levine, Assistant Professor
My research is in lowdimensional topology, the study of the shapes of 3 and 4dimensional spaces (manifolds) and of curves and surfaces contained therein. Classifying smooth 4dimensional 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 4manifolds, 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 3space, particularly the connections between knot invariants arising from gauge theory and symplectic geometry and those coming from representation theory.  Contact Info:
Teaching (Fall 2019):
 MATH 221.02, LINEAR ALGEBRA & APPLICA
Synopsis
 Physics 119, TuTh 08:30 AM09:45 AM
 (also crosslisted as MATH 721.02)
 Office Hours:
 Tuesdays, 1:303:00 pm
Thursdays, 9:3011:00 am
 Education:
Ph.D.  Columbia University  2010 
A.B.  Harvard University  2005 
 Keywords:
Floer homology • Knot theory • Lowdimensional topology • Topology
 Recent Publications
(More Publications)
 Levine, AS; Lidman, T, SIMPLY CONNECTED, SPINELESS 4MANIFOLDS,
Forum of Mathematics, Sigma
(January, 2019) [doi] [abs]
 Levine, AS; Ruberman, D, Heegaard Floer invariants in codimension one,
Transactions of the American Mathematical Society
(2018),
pp. 11, American Mathematical Society (AMS) [doi]
 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. 17400041740004, World Scientific Pub Co Pte Lt [doi] [abs]
 Greene, J; Levine, A, Strong Heegaard diagrams and strong Lâ€“spaces,
Algebraic & Geometric Topology, vol. 16 no. 6
(December, 2016),
pp. 31673208, Mathematical Sciences Publishers [doi]
 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
 LowDimensional topology, Floer Homology, and Categorification, National Science Foundation, DMS1806437year 1, 2017/072020/04.
