**Fernando Coda-Marques**

[Together with Andre Neves he proved][1] the [Willmore conjecture][2]. This states that the Clifford torus in the 3-sphere minimizes the Willmore energy, with energy $2\pi^2$. To prove this conjecture, they show that for 5-parameter sweepouts of $S^3$ by surfaces, with certain boundary conditions, the min-max area is $2\pi^2$. This theorem has [other consequences][3] besides the Willmore conjecture.  


  [1]: http://annals.math.princeton.edu/2014/179-2/p06
  [2]: http://en.wikipedia.org/wiki/Willmore_conjecture
  [3]: https://arxiv.org/abs/1205.0825