Type: Seminar

Modified: Tue 12 Jun 2012 2310

Distribution: World

Expiry: 29 Jun 2012

CalTitle1: Geometry Seminar: Carberry -- The Periodicity Problem for Harmonic Maps of the Plane

Auth: zhangou@bari.maths.usyd.edu.au

This event has been postponed due to people’s other duties. Sorry about any inconvenience. ----------------------------------------------------------------------- Speaker: Dr. Emma Carberry (Sydney) Time: Tuesday, June 12, 12(NOON)--1PM Room: Carslaw 159 Lunch: after the talk (at Taste at Sydney Uni, i.e. "Law School Annex Cafe") --------------------------------------------------- Title: The Periodicity Problem for Harmonic Maps of the Plane Abstract: harmonic maps from the complex plane to a Lie group or symmetric space form an integrable system, and hence we expect that there are some solutions which are simpler than the general ones and can be found explicitly. A particularly useful encoding of this fact is the spectral curve of a harmonic map of finite type, which expresses what was initially a problem in differential geometry purely in terms of algebraic geometry. This introduces a number of new techniques, and is in particular better adapted for addressing moduli space questions. Not all maps of the plane can be expressed in this way, but for various target spaces it is known that all doubly periodic such maps (ie maps of 2-tori) can be studied using spectral curves. We will explain how studying the periodicity of the harmonic map in terms of its spectral curve leads to an understanding of the moduli space of such harmonic maps. We will focus on the examples of minimal and constant mean curvature surfaces in the 3-sphere. --------------------------------------------------- Web site for Geometry Seminar is at: http://www.maths.usyd.edu.au/u/SemConf/Geometry/index.html