Abstract:

Special Lagrangians are a certain class of area-minimizing Lagrangians in Calabi--Yau manifolds which is discovered by Harvey and Lawson about 1980 and has been playing an important role in geometry and string theory. One fundamental question about special Lagrangians is to find such a nice compactification of moduli spaces of special Lagrangians as in the counting of Yang-Mills anti-self-dual instantons or pseudo-holomorphic curves. Geometry measure-theory provides a natural notion of singular special Lagrangians and compact moduli-spaces but the treatment of singularities in this sense is considerably more difficult than those of Yang--Mills instantons or holomorphic curves. On the other hand the recent progress on Fukaya-categories in symplectic geometry helps indeed to study the singularities of special Lagrangians. Some of these topics will be explained in the seminar.