- Phillip Griffiths Assistant Research Professor
- Assistant Research Professor of Mathematics
Tuesdays 5 to 7pm, or by appointment
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.
Ni, Y., and F. Vafaee. “Null surgery on knots in L-spaces.” Transactions of the American Mathematical Society, vol. 372, no. 12, Dec. 2019, pp. 8279–306. Scopus, doi:10.1090/tran/7510. Full Text Open Access Copy
Donald, A., et al. “On L-space knots obtained from unknotting arcs in alternating diagrams.” New York Journal of Mathematics, vol. 25, Jan. 2019, pp. 518–40. Open Access Copy
Donald, A., and F. Vafaee. “A slicing obstruction from the 10/8 theorem.” Proceedings of the American Mathematical Society, vol. 144, no. 12, Jan. 2016, pp. 5397–405. Scopus, doi:10.1090/proc/13056. Full Text Open Access Copy
Vafaee, F. “Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic.” Topology and Its Applications, vol. 184, Apr. 2015, pp. 72–86. Scopus, doi:10.1016/j.topol.2015.01.005. Full Text Open Access Copy
Hom, J., et al. “Berge–Gabai knots and L–space satellite operations.” Algebraic and Geometric Topology, vol. 14, no. 6, Jan. 2015, pp. 3745–63. Scopus, doi:10.2140/agt.2014.14.3745. Full Text Open Access Copy
Vafaee, F. “On the Knot Floer Homology of Twisted Torus Knots.” International Mathematics Research Notices, vol. 2015, no. 15, Jan. 2015, pp. 6516–37. Scopus, doi:10.1093/imrn/rnu130. Full Text Open Access Copy