Geometry Seminar : Carberry -- Integrable Systems and Harmonic Maps

Speaker: Dr. Emma Carberry (Sydney)

Time: Tuesday, October 4th, 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 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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