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.

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 |

**Teaching (Fall 2018):**

- MATH 611.01,
*ALGEBRAIC TOPOLOGY I*Synopsis- Physics 227, TuTh 08:30 AM-09:45 AM

**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**- Baldwin, JA; Levine, AS; Sarkar, S,
*Khovanov homology and knot Floer homology for pointed links*, Journal of Knot Theory & Its Ramifications, vol. 26 no. 02 (February, 2017), pp. 1740004-1740004 [doi] - Greene, J; Levine, A,
*Strong Heegaard diagrams and strong L–spaces*, Algebraic and Geometric Topology, vol. 16 no. 6 (December, 2016), pp. 3167-3208 [doi] - Hedden, M; Levine, AS,
*Splicing knot complements and bordered Floer homology*, Journal für die Reine und Angewandte Mathematik (Crelle's Journal), vol. 2016 no. 720 (January, 2016) [doi] - LEVINE, ADAMSIMON,
*NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE*, Forum of Mathematics, Sigma, vol. 4 (2016) [doi] - Levine, A; Ruberman, D; Strle, S,
*Nonorientable surfaces in homology cobordisms*, Geometry and Topology, vol. 19 no. 1 (February, 2015), pp. 439-494 [doi]

- Baldwin, JA; Levine, AS; Sarkar, S,

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