# Adam S. Levine

- Assistant Professor of Mathematics

**External address:**120 Science Drive, 211 Physics Building, Durham, NC 27708

**Phone:**(919) 660-2802

### Research Areas and Keywords

##### Topology

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.

### Selected Grants

Low-Dimensional topology, Floer Homology, and Categorification awarded by National Science Foundation (Principal Investigator). 2017 to 2020

Baldwin, JA, Levine, AS, and Sarkar, S. "Khovanov homology and knot Floer homology for pointed links." *Journal of Knot Theory and Its Ramifications* 26.02 (February 2017): 1740004-1740004.
Full Text

Greene, J, and Levine, A. "Strong Heegaard diagrams and strong L–spaces." *Algebraic & Geometric Topology* 16.6 (December 15, 2016): 3167-3208.
Full Text

Hedden, M, and Levine, AS. "Splicing knot complements and bordered Floer homology." *Journal für die reine und angewandte Mathematik (Crelles Journal)* 2016.720 (January 1, 2016).
Full Text

LEVINE, ADAMSIMON. "NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE." *Forum of Mathematics, Sigma* 4 (2016).
Full Text

Levine, A, Ruberman, D, and Strle, S. "Nonorientable surfaces in homology cobordisms." *Geometry & Topology* 19.1 (February 27, 2015): 439-494.
Full Text

Baldwin, JA, and Levine, AS. "A combinatorial spanning tree model for knot Floer homology." *Advances in Mathematics* 231.3-4 (October 2012): 1886-1939.
Full Text

Levine, AS. "Slicing mixed Bing-Whitehead doubles." *Journal of Topology* 5.3 (September 2012): 713-726.
Full Text

Levine, AS. "Knot doubling operators and bordered Heegaard Floer homology." *Journal of Topology* 5.3 (September 2012): 651-712.
Full Text

LEVINE, ADAMSIMON. "ON KNOTS WITH INFINITE SMOOTH CONCORDANCE ORDER." *Journal of Knot Theory and Its Ramifications* 21.02 (February 2012): 1250014-1250014.
Full Text

Levine, AS, and Lewallen, S. "Strong L-spaces and left-orderability." *Mathematical Research Letters* 19.6 (2012): 1237-1244.
Full Text