## Symplectic forms in algebraic geometry

Giulia Saccà

Member, School of Mathematics

January 30, 2015

Imposing the existence of a holomorphic symplectic form on a projective algebraic variety is a very strong condition. After describing various instances of this phenomenon (among which is the fact that so few examples are known!), I will focus on the specific topic of maps from projective varieties admitting a holomorphic symplectic form. Essentially, the only such maps are Lagrangian fibrations and birational contractions. I will motivate why one should care about these types of maps, and give many examples illustrating their rich geometry.