SMS scnews item created by Haotian Wu at Wed 26 Feb 2020 1642
Type: Seminar
Modified: Thu 27 Feb 2020 1124
Distribution: World
Expiry: 27 May 2020
Calendar1: 27 Feb 2020 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Geometry and Topology Seminar: Ogilivie -- Willmore tori and their spectral curves
Auth: haotianw@ (hawu2800) in SMS-WASM

Geometry and Topology Seminar

Willmore tori and their spectral curves

Ogilivie (Mannheim)

Thursday, 27 Feb 2020, 12:00–13:00, in Carslaw 535.

Seminar schedule

Please join us for lunch after the talk.

Abstract: In this talk we discuss the Willmore functional of surfaces in R^3, S^3, and R^4. It is the integral of the square of mean curvature. Treating 2-tori in particular, we show that a generalisation of the Weierstrass representation of minimal surfaces can be used to define a spectral curve. Spectral curves are algebraic curves that encode the information about a surface. We then consider how to deform these spectral curves, so called Whitham deformations. We finish with what these deformations can tell us about the moduli space of harmonic maps, of surfaces with constant mean curvature, and perhaps of Willmore surfaces.