Joint Colloquium: Morrison -- Birational Geometry of Moduli Spaces of Curves

Moduli spaces are one of the beauties of algebraic geometry: SETS of isomorphism classes
that turn out to carry a natural ALGEBRAIC structure.  Many general questions are of
special interest for such moduli spaces and lead to a beautiful interplay between the
geometry of the objects individually and in families.  In my talk, I will try to
introduce and illustrate these ideas.  The moduli spaces I will discuss are those of
algebraic curves --- widely studied and applied in mathematical physics, symplectic
geometry and number theory.  The questions I will ask about them are from birational
geometry and deal with maps from these spaces to complex projective spaces.