Hints and tips:
  • You may need to look up some unfamiliar terms in the title or description to get more of a sense of what is involved.
  • If the project has "No" in the "Current Availability:" field, it is already taken or not being offered this academic year but may be available again in future years.
  • The supervisor name links to a contact details webpage so, if you are interested, you can arrange to discuss this project or even propose a related topic of your own.
Level: BSc, MSci, MSc
Title: The Lawson conjecture
Supervisor:

Dr Reto Buzano
Research Area: Geometry and Analysis
Description:

In 1970, Lawson conjectured that every embedded minimal torus in the three-sphere S3 is congruent to the Clifford torus. This conjecture was recently proved by Simon Brendle using a very elegant trick to reduce the problem to only studying rotationally symmetric tori. Depending on your level (Third-year or Masters), in this project you are working out the details of some parts of this proof or the full proof.
Further Reading:
  • S. Brendle, Embedded minimal tori in S^3 and the Lawson conjecture, Acta Mathematica, 211 2 (2013) 177–190.

Other references will be provided, depending on the level of the student and the precise goal of the project.
Key Modules:

MTH5109 Geometry II: Knots and Surfaces

MTH5104 Convergence and Continuity
Other Information:

If you take this as an MSci or MSc student (and are thus expected to also work on the more analytical parts of the proof of the conjecture), you should have a rather solid background in Calculus and Analysis (at the very least MTH5104 Convergence and Continuity).
Current Availability: Yes