Contact DetailsSchool of Mathematics and Statistics
University of Sheffield
Sheffield S3 7RH
Telephone: +44 (0)114 222 3872
Email: f.roukema (at) sheffield.ac.uk
I am a research and teaching associate in mathematics at the University of Sheffield.
I am a pure mathematician with research interests in low dimensional topology.
I am enthusiastic about learning and teaching mathematics; my office is K12 Hicks Building and
you should feel welcome to pop in if you would like to chat about mathematics.
As an undergraduate I studied at the University of Edinburgh and the University of California at Berkeley, and as a graduate student I studied at the University of Cambridge, the University of Toronto and at the University of Pisa. I completed my Ph.D. in 2011 under the supervision of Prof. Carlo Petronio and Dr. Bruno Martelli at the University of Pisa. You can find out more about what I have done and where I have been in my curriculum vitae.
In addition to mathematics I have passions for travel, wildlife, good food, good coffee, and good company.
My mathematical interests lie in low dimensional topology. To date all my work has connected to
knot theory; I have worked on problems in Dehn surgery and the geometry of 3-manifolds, virtual
knot theory, and finite type invariants. I intend to continue working on problems in these
areas and to broaden my knowledge base. In particular, I hope to learn more about Khovanov and
Heegaard Floer homology theories.
My Ph.D. is available here and my (pre)prints can be found here. A very brief overview of my work, past and present, and the future direction that my research will take can be found in my research statement.
During the 2013-2014 academic year I am teaching:
I am passionate about promoting mathematics and widening mathematical participation. Here are some of the ways that I have helped to promote a love for mathematics:
I have worked on projects with Dror Bar-Natan,
Bruno Martelli, and I am beginning
a collaboration with mathematicians at Aix-Marseille University.
SnapPy, written by Marc Culler, Nathan Dunfield and Jeff Weeks, is a wonderful mathematical programme if you are interested in hyperbolic 3-manifolds, and this makes a good addition if you are interested in enumerating all exceptional surgery instructions on a link complement in the 3-sphere.