Marianty Ionel, McMaster University, September 16, 2002
Title: Special Lagrangian Submanifolds in C^m
Abstract:
Special lagrangian geometry received reinforced attention in 1996 because
of the SYZ conjecture. This conjecture reveals the role of the special
lagrangian geometry in Mirror Symmetry, a mysterious relationship between
pairs of Calabi-Yau 3-folds, coming from String Theory. In this context, a
lot of research is going on to find as many examples of special lagrangian
submanifolds as possible, in order to understand what kind of
singularities they can develop, classify them and ultimately resolve the
SYZ conjecture. Because singularities of SL m-folds in Calabi-Yau are
locally modeled on singularities of SL m-folds in C^m, the first step
would be to understand and classify SL in C^m. In dimension m=2, the
classification is done and a lot of examples are known in higher
dimensions by now, but a complete classification is not yet known, even
for dimension m=3.
This talk will introduce the notion of a special lagrangian submanifold
in a Calabi-Yau manifold, some basic properties and some known examples in
the flat case C^m, with an accent to the dimension m=3, of interest to
physicists.