Home » Lectures » Mohammed Abouzaid: Lectures

Mohammed Abouzaid: Lectures

September 10, 2021
TITLE: Lagrangian fibrations from the perspective of Floer theory

ABSTRACT: While the construction of special Lagrangian fibrations remains largely open in higher dimensions, we have achieved significant progress in the last decade in constructing singular Lagrangian fibrations on large classes of symplectic manifolds, and understanding the associated Floer theoretic invariants. I discuss these developments and their mirror symmetry motivations, and touch upon questions related to the existence of special Lagrangians.

Slides of Lecture

June 4, 2019
TITLE: On nearby special Lagrangians

Given a closed, embedded, special Lagrangian in a Calabi-Yau
manifold, we consider the question of classifying the C0-close (nearby) special
Lagrangians. The corresponding classification result in the C topology is
classical, as such Lagrangians correspond to the graphs of harmonic 1-forms. I
shall explain that, if the fundamental group of the Lagrangian is nilpotent, then
all embedded nearby Lagrangians which are unobstructed in the sense of Floer
theory are given by this construction, and will explain some basic examples of
unobstructed Lagrangians which are not graphical in some cases where the
fundamental group is not nilpotent. The proof relies on methods of geometric
analysis and Floer theory, building upon the ideas of Thomas and Yau. This is
joint work with Yohsuke Imagi.