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# Benjamin Bakker, Hodge Theory and Lagrangian Fibrations

## April 29 @ 4:00 pm - 5:00 pm KST

B236-1,
IBS
Korea, Republic of

*X* are higher-dimensional generalizations of *K*3 surfaces; their geometry is tightly constrained by the existence of a holomorphic symplectic form. For example, a result of Matsushita says the only nontrivial fibration structures *f*:*X*→*B* they admit are fibrations by Lagrangian tori. In this talk, I will give an overview of how Hodge theory connects the geometry of *B* to the variation of these tori in moduli, and how Hodge-theoretic techniques can be used to understand *B* both locally and globally.