Princeton University Mathematics Department Colloquium

Picard-Lefschetz theory studies algebraic varieties by induction on their dimension. It can be used to determine their topology, and in more modern terms their symplectic geometry. We will apply this theory to describe extra structure which appears for a special class of algebraic varieties. This is part geometry and part homological algebra; the latter appears because the outcome is formulated in terms of actions of algebraic groups on categories.