Fionntan Roukema Homepage
Fionntan Roukema

Contact Details

School of Mathematics and Statistics
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield S3 7RH
United Kingdom

Telephone: +44 (0)114 222 3872

Email: f.roukema (at)

About me

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:

  • MAS5050 Mathematical Methods for Statistics throughout the year. Course material for this module can be accessed via MOLE.
  • MAS277 Vector Spaces and Fourier Theory in Semester 2. Course material for this course will be made available here.
  • MAS205 Statistics Core at Nanjing Univeristy of Technology in Semester 2. This module is taught as part of the joint NJUT-Sheffield B.Sc. in Financial Mathematics. The syllabus for the module can be found here.
An overview of my teaching experience from previous years and my general teaching philosophy can be found in my teaching statement.

Further mathematical engagement

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:

  • Together with Jayanta Manoharmayum we launched the SoMaS take home team competition.
  • Eugenia Cheng set up the Maths Academy in 2011 to promote learning for the love of learning in a non-exam based setting. I got involved with the Maths Academy in 2012, and I am running the project during the 2013-2014 academic year while Eugenia is on study leave. You can find a promotional flyer for the project here, and details for 2013-2014 can be found here.
  • During the 2012-2013 academic year I helped Dennis Almeida (the SoMaS outreach officer) to set up a STEP preparation course. The result was a SoMaS staff and student collaboration which produced a lovely series of notes, problems and sessions to guide secondary school students through their STEP preparation. The students who attended the course and took STEP typically did well above their expectations. The timetable of this years sessions can be found here.
  • I have promoted mathematics outside of the standard university setting: I have written pieces for Mathematical Spectrum, and I have appeared on the Mikie Show to speak about and promote mathematics.


I have worked on projects with Dror Bar-Natan, Carlo Petronio, 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.

Disclaimer: Information on this site may be out of date.