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## Faramarz Vafaee, Phillip Griffiths Assistant Research Professor

My main research interests lie in low dimensional topology and geometry. Among others, these interests include Heegaard Floer homology and its applications, Khovanov homology, contact and symplectic geometry, and handlebody theory.

A central goal of low dimensional topology is to understand three and four–dimensional spaces. Achieving this understanding is often aided through the study of knots and surfaces embedded therein, and the theory of knotted curves and surfaces have become fields in their own right. The past thirty years have witnessed the births of a beautiful array of approaches to the field, drawing on diverse tools from algebra, analysis, and combinatorics. One particular tool that has made a dramatic impact on low-dimensional topology is the Heegaard Floer theory of Ozsvath and Szabo. Defined 17 years ago, this theory has produced an encompassing package of invariants, which have significantly impacted the study of many areas of low dimensional topology. Among these are Dehn surgery and foliation theory, and a central theme within my work aims to better understand and exploit the interaction between Floer homology and these areas.

Contact Info:
 Office Location: 120 Science Drive, 246 Physics Building, Durham, NC 27708 Office Phone: (919) 660-2873 Email Address: Web Pages: https://sites.google.com/view/faramarz-vafaee/homehttps://sites.google.com/view/faramarz-vafaee/teaching

Teaching (Spring 2019):

• MATH 212.03, MULTIVARIABLE CALCULUS Synopsis
Physics 119, TuTh 08:30 AM-09:45 AM
(also cross-listed as MATH 712.03)
• MATH 212.04, MULTIVARIABLE CALCULUS Synopsis
Bio Sci 130, TuTh 11:45 AM-01:00 PM
(also cross-listed as MATH 712.04)
Office Hours:

Tuesdays 5 to 7pm, or by appointment
Education:

 Ph.D. Michigan State University 2014
Recent Publications

1. Greene, JE; Lewallen, S; Vafaee, F, (1, 1) L-space knots, Compositio Mathematica, vol. 154 no. 5 (May, 2018), pp. 918-933, Oxford University Press (OUP) [doi]  [abs]
2. Donald, A; Vafaee, F, A slicing obstruction from the $\frac {10}{8}$ theorem, Proceedings of the American Mathematical Society, vol. 144 no. 12 (August, 2016), pp. 5397-5405, American Mathematical Society (AMS) [doi]
3. Vafaee, F, Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic, Topology and Its Applications, vol. 184 (April, 2015), pp. 72-86, Elsevier BV [doi]
4. Hom, J; Lidman, T; Vafaee, F, Berge–Gabai knots and L–space satellite operations, Algebraic & Geometric Topology, vol. 14 no. 6 (January, 2015), pp. 3745-3763, Mathematical Sciences Publishers [doi]
5. Vafaee, F, On the Knot Floer Homology of Twisted Torus Knots, International Mathematics Research Notices, vol. 2015 no. 15 (January, 2015), pp. 6516-6537, Oxford University Press (OUP) [doi]  [abs]

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320