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Title: Examples of special Lagrangians in asymptotically conical Calabi-Yau manifolds

Speaker: Alessio Di Lorenzo

Abstract: Special Lagrangians are submanifolds of (almost) Calabi-Yau manifolds that sit at the intersection of calibrated and complex geometry. They are generally speaking hard to find, and it is conjectured (Thomas-Yau conjecture) that the existence of special Lagrangians is equivalent to a certain algebraic stability condition. We will focus on the case of asymptotically conical Calabi-Yau manifolds, of which important examples are smoothings of Calabi-Yau cones.

Smoothing out nodes in singular Calabi-Yau manifolds gives birth to special Lagrangians for “close enough” smoothings in the space of versal deformations, via a gluing construction. We will show some examples of this phenomenon, which is one way of constructing special Lagrangians, in the asymptotically conical case. We will compare this gluing construction with another way of constructing special Lagrangians, which is via considering fixed loci of antisymplectic involutions.

Some snacks will be provided before and after the talk.

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