Department of Mathematics - Master Calendar

Title: New Minimal Lagrangians in ℂℙ² 

Abstract: Minimal Lagrangian tori in ℂℙ² are the expected local model for particular point singularities of Calabi-Yau 3-folds, and numerous examples have been constructed. In stark contrast, very little is known about higher genus examples, with the only ones to date due to Haskins-Kapouleas and only in odd genus. Using loop group methods, we construct new examples of minimal Lagrangian surfaces of genus (k-1)(k-2)/2 for large k, hence providing the first examples in even genus. Time permitting, we show our surfaces lift to embedded special Legendrian surfaces in the 5-sphere. These are the first embedded examples. This is joint work with Sebastian Heller and Franz Pedit.