# A cone conjecture for log Calabi-Yau surfaces

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Jennifer Li, University of Massachusetts Amherst

Zoom link:  https://princeton.zoom.us/j/91248028438

In 1993, Morrison conjectured that the automorphism group of a Calabi-Yau 3-fold acts on its nef cone with a rational polyhedral fundamental domain. In this talk, I will discuss a version of this conjecture for log Calabi-Yau surfaces that we have proved. In particular, for a generic log Calabi-Yau surface with singular boundary, the monodromy group acts on the nef effective cone with a rational polyhedral fundamental domain. In addition, the automorphism group of the unique surface with a split mixed Hodge structure in each deformation type acts on the nef effective cone with a rational polyhedral fundamental domain.