Geometry Seminar: Carberry -- The Periodicity Problem for Harmonic Maps of the Plane (Postponed)

This event has been postponed due to people’s other duties. 
Sorry about any inconvenience.

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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")

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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. 

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Web site for Geometry Seminar is at: 

http://www.maths.usyd.edu.au/u/SemConf/Geometry/index.html