# Harmonic Tori in Compact Lie Groups and Symmetric Spaces

#### by Emma Carberry

Institution: University of Melbourne
Date: Mon 24th October 2005
Time: 3:15 PM
Location: Theatre 1, Old Geology Building, The University of Melbourne

Abstract: Harmonic maps from a 2-torus to a compact Lie group or symmetric space
form an integrable system and many such maps permit a purely
algebro-geometric description, in terms of a linear flow on the Jacobian
of an algebraic curve. I will explain how (in work with Ian McIntosh) this
point of view was used to prove the existence of real n-dimensional
families of special Lagrangian $T^2$-cones in $\mathbb{C}^3$, for all
positive integers n. These cones provide the first order model for the
singularities that can occur in the foliations Calabi-Yau 3-folds by
special Lagrangian 3-tori featured in the Strominger-Yau-Zaslow conjecture
of string theory. I will also describe work-in-progress with Erxiao Wang
in which we are establishing and exploiting an algebro-geometric
description of almost complex tori in $S^6$, or equivalently of
associative $T^2$-cones in the imaginary octonions.