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 lowdimensional 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 Hours:
 Tuesdays 5 to 7pm, or by appointment
 Education:
Ph.D.  Michigan State University  2014 
 Recent Publications
(More Publications)
 Donald, A; McCoy, D; Vafaee, F, On Lspace knots obtained from unknotting arcs in alternating diagrams,
New York Journal of Mathematics, vol. 25
(January, 2019),
pp. 518540, ELECTRONIC JOURNALS PROJECT
 Greene, JE; Lewallen, S; Vafaee, F, (1, 1) Lspace knots,
Compositio Mathematica, vol. 154 no. 5
(May, 2018),
pp. 918933, Oxford University Press (OUP) [doi] [abs]
 Donald, A; Vafaee, F, A slicing obstruction from the 10/8 theorem,
Proceedings of the American Mathematical Society, vol. 144 no. 12
(January, 2016),
pp. 53975405, American Mathematical Society (AMS) [doi] [abs]
 Vafaee, F, Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic,
Topology and Its Applications, vol. 184
(April, 2015),
pp. 7286, Elsevier BV [doi] [abs]
 Hom, J; Lidman, T; Vafaee, F, Berge–Gabai knots and L–space satellite operations,
Algebraic & Geometric Topology, vol. 14 no. 6
(January, 2015),
pp. 37453763, Mathematical Sciences Publishers [doi] [abs]
