Description
In the first part of the talk, starting from basic notions, I will introduce special Lagrangian submanifolds, due to Harvey and Lawson. These play an important role in the calculus of variations and in string theory. Around the year 2000, R. Thomas and S.-T. Yau proposed a conjectural criterion for the existence of a special Lagrangian submanifold in a suitable fixed isotopy class. In the second part of the talk I will sketch the current viewpoint of this conjecture, due to D. Joyce and Y. Li, mentioning some positive results for a class of examples with toric symmetry.
