Columbia Mathematics Department Colloquium


Picard-Lefschetz theory
and hidden group actions


Paul Seidel




Classical Picard-Lefschetz theory (from about 1920) provides a way of computing the
homology of affine algebraic varieties by dimensional induction. It
determines not just the homology groups themselves, but also the intersection pairing.
Recent advances in symplectic topology indicate that a certain class of affine varieties admits hidden symmetries (not realized by geometric group actions), which
allows one to define q-deformed intersection pairings. We adapt the framework of
Picard-Lefschetz theory to construct and compute such pairings.


Wednesday, Apr 9, 5:00 - 6:00 p.m.
Mathematics 520
Tea will be served at 4:30 p.m.