Paul Hacking (UMass): Mirror symmetry and moduli of Calabi--Yau 3-folds

The recent preprint of Bakker-Filipazzi-Mauri-Tsimerman constructs a compactification of the moduli space of Calabi--Yau manifolds analogous to the Baily--Borel compactification for K3 surfaces, proving conjectures of Green--Griffiths--Robles--Laza. In 1993 David Morrison envisaged a compactification of the moduli space of Calabi--Yau 3-folds near a so-called large complex structure limit point based on mirror symmetry heuristics. We will explore the connection between the BFMT compactification and the conjectural compactification of Morrison for Calabi--Yau 3-folds. I will attempt to keep prerequisites to a minimum.