Frédéric Rochon, UQAM University of Quebec
“The moduli space of asymptotically cylindrical Calabi-Yau manifolds”
We show that the examples of asymptotically cylindrical Calabi-Yau manifolds recently obtained by Haskins-Hein-Nordstrom admit a full polyhomogeneous expansion at infinity. Making use of the b-calculus of Melrose, we then establish at Tian-Todorov result in that context, namely, we show that the deformation theory of such complex manifolds is unobstructed. Time permitting, we will also discuss how to define the Weil-Peterson metric in that context as well as some of its properties. This is a joint work with Ronan Conlon and Rafe Mazzeo.