SMS scnews item created by Zhou Zhang at Wed 5 Oct 2011 1542
Type: Seminar
Distribution: World
Expiry: 19 Oct 2011
Calendar1: 11 Oct 2011 1200-1300
CalLoc1: Carslaw 707A
Auth: zhangou@bari.maths.usyd.edu.au

# Geometry Seminar: Carberry -- Integrable Systems and Harmonic Maps

Geometry Seminar : Carberry -- Integrable Systems and Harmonic Maps

Speaker: Dr. Emma Carberry (Sydney)

Time: Tuesday, October 11th, 12(NOON)--1PM

Room: Carslaw 707A

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Series Title: Integrable Systems and Harmonic Maps

Abstract: in this expository series of talks I will
give a tour of the theory of harmonic maps from
surfaces into Lie groups and symmetric spaces. This
subject brings together integrable systems, differential
geometry and complex algebraic geometry. It also has
connections with mathematical physics, in fact these
harmonic map equations are a reduction of the Yang-Mills
equations with a change of signature from the reduction
that describes Higgs bundles on a Riemann surface. Of
particular interest are harmonic maps of tori, which
in many cases can be obtained simply by solving
ordinary differential equations and whose moduli spaces
can be constructed quite explicitly.

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Lecture 2 (October. 11)

Title: Harmonic Maps Via Ordinary Differential Equations

Abstract: harmonic maps are by definition the solutions
to the Laplace-Beltrami equation, a second order partial
differential equation. However there is a subclass of
harmonic maps from a surface to a Lie group or symmetric
space which can be described by vastly easier means.
These maps of "finite-type" are obtained simply by
integrating a pair of commuting vector fields on a finite
dimensional space and hence by solving ordinary differential
equations. This naturally prompts one to find conditions
under which a map is of finite type, for which there are
quite general results known when the target manifold is
compact.

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Lecture 1 (October 4th)

Title: Introduction to Harmonic Maps of Surfaces Into
Lie Groups and Symmetric Spaces

Abstract: in this talk I will explain some basic facts
about harmonic maps, concentrating on the geometrically
interesting situation of mapping a surface into a Lie
group or symmetric space. In this case the harmonic
condition is equivalent to a certain family of connections
all having zero curvature, which is the basis for the
integrable systems approach to the subject.

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