Departmental Colloquium
Richard Hain
Duke University
Mapping class groups and rational points of algebraic curves
Abstract: In this talk I will discuss the beginnings of a theory of
characteristic classes of rational points of smooth projective curves.
This theory is analogous to the theory of characteristic classes of
vector bundles in which grassmanians are replaced by moduli spaces of
curves. I will concentrate on the case where $C$ is defined over the
function field of another curve $T$. In this case, the curve corresponds
to a family $X\to T$ of smooth projective curves over $T$. Rational
points of $C$ correspond to sections of the family $X\to T$. Such
families are classified by maps from $T$ into the moduli space of curves
and rational points of $C$ correspond to lifts of this map to the moduli
space of 1-pointed curves. Mapping class groups are groups of isotopy
classes of diffeomorphisms of a compact oriented surface. They enter
the story as the cohomology of these moduli spaces is the cohomology
of mapping class groups.
Friday October 19, 2012 at 3:00 PM in SEO 636