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AG Geometrische Analysis (Winter Semester 2018/19)

Seminar: Tuesday 14:00-15:30 SR 2.67
  • November 6th 2018 (Tuesday), 2pm (SR 2.067): Fritz Hiesmayr (University of Cambridge)

Title: Index bounds in the Allen-Cahn construction

In the Allen-Cahn construction one constructs minimal surfaces as the
weak limit of level sets of a semilinear elliptic PDE, called the Allen-Cahn
equation. In this talk I will give a brief overview of the Allen-Cahn
theory, and then present my work relating the variational properties
of the solutions of the Allen-Cahn equation to the surface arising in
the limit. For example, the minimal surface inherits index bounds from
a sequence of unstable critical points; time permitting I will sketch a
proof of this.