Prof. Ivan Smith
(Cambrigde)
Symplectic linear systems
Abstract:
This sequence of four lectures will discuss
the geometry of Lefschetz fibrations on symplectic manifolds
concentrating on dimension four. We will sketch Donaldson's
approximately holomorphic geometry algebraic invariants (and perhaps
categorical ones) and end by describing how to obtain symplectic
surfaces in four manifolds using these methods. This in particular
reproves various theorems of Taubes from Seiberg-Witten Theory.
Titles of lectures:
L1 Introduction to Lefschetz fibrations
L2 Approximately holomorphic geometry
L3 Algebraic Invariants
L4 Symmetric products and the canonical class