Mathematics Colloquium

The idea of studying Floer cohomology for families of
Lagrangians was suggested by Kontsevich and Fukaya as a strategy for
unifying the homological and geometric approaches to mirror symmetry.
I will explain the heuristics, the major technical problems that have
prevented progress, and some recent results resolving these problems.
Finally, with generalizations to the non-commutative setting in mind,
I will explain a new approach to the study of Family Floer cohomology
which focuses on functions instead of points.