Level: BSc, MSci, MSc
Title: The Lawson conjecture
Supervisor:
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:
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