# Index and spectrum of minimal hypersurfaces arising from the Allen-Cahn construction

**Date**: Wednesday 25 October 2017, 15:00 – 16:00**Location**: Roger Stevens LT 09 (8M.09)**Type**: Pure Mathematics seminars, Geometry seminars, Seminar series**Cost**: Free

#### Fritz Hiesmayr, University of Cambridge. Part of the geometry seminar series.

The Allen-Cahn construction is a method for constructing minimal surfaces of codimension 1 in closed manifolds. In this approach, minimal hypersurfaces arise as the weak limits of level sets of critical points of the Allen-Cahn energy functional. In my talk, I will give a brief overview of this construction, and then present my work relating the variational properties of the hypersurfaces arising in the limit to those of the Allen-Cahn energy functional. For instance, bounds for the Morse indices of the critical points lead to abound for the Morse index of the limit minimal surface; time permitting I will sketch a proof of this.

**Fritz Hiesmayr, ***University of Cambridge*