##### Department of Mathematics,

University of California San Diego

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### Joint UCI-UCR-UCSD Geometry Seminar

## Yu-Shen Lin

#### Boston University

## skyeSpecial Lagrangian fibrations in weak Del Pezzo Surfaces

##### Abstract:

Motivated by the study of mirror symmetry, Strominger-Yau-Zaslow (SYZ) conjectured that Calabi-Yau manifolds admit certain minimal Lagrangian fibrations. These minimal Lagrangians are the special Lagrangian submanifolds studied earlier by Harvey-Lawson. Many of the implication of the SYZ conjecture is proved and it has been the guiding principle for studying mirror symmetry for a long time. However, not many special Lagrangians are known in the literature. In this talk, I will prove the existence of special Lagrangian fibration on the complement of a smooth anti-canonical divisor in a (weak) Del Pezzo surface. If the time allows, I will explain its impact to mirror symmetry. This is joint work with Tristan Collins and Adam Jacob.

### June 4, 2019

### 4:00 PM

### UCR

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