# 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

Levine, AS, and Ruberman, D. "Heegaard Floer invariants in codimension one." *Transactions of the American Mathematical Society* (2018): 1-1.
Full Text

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 Open Access Copy

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

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 Open Access Copy

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

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

Levine, AS, and Ruberman, D. "Generalized Heegaard Floer correction terms." *Proceedings of the Gökova Geometry Topology Conference 2013* (May 12, 2014): 76-96.
Open Access Copy

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 Open Access Copy

Levine, AS. "Slicing mixed Bing-Whitehead doubles." *Journal of Topology* 5.3 (September 2012): 713-726.
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Levine, AS. "Knot doubling operators and bordered Heegaard Floer homology." *Journal of Topology* 5.3 (September 2012): 651-712.
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