EVENT DETAILS AND ABSTRACT

Title: Algebraic geometry techniques in symplectic geometry
Speaker: Professor Ludmil Katzarkov
Speaker Info: University of California, Irvine
Brief Description:
Special Note:
Abstract:

Recent remarkable results of Donaldson show that every four-dimensional symplectic manifold has the structure of a symplectic Lefschetz pencil. The analogy with projective surfaces opens a new direction in the investigation of four-dimensional symplectic manifolds.

In this talk, we explain Donaldson's results, and use them to construct symplectic maps to CP^2. This allows us to adapt the braid monodromy techniques of Moishezon and Teicher from the projective case to the symplectic case. We show that classification of four-dimensional symplectic manifolds can be reduced to certain a combinatorial result about braid groups.

As a consequence, we show the existence of infinitely many "symplectic" curves in CP^2 with the same degree and the same number of cusps and nodes, but whose complements have different fundamental groups.