Deformation theory and moduli spaces of abelian varieties in positive
characteristic (Elena Mantovan, Berkeley)

The theory of abelian varieties is a very classical topic in algebraic
geometry which plays a fundamental role in number theory, and in
particular in the Langlands program.  Abelian varieties in positive
characteristic exhibit interesting features not seen in characteristic
zero.  In my working group, we will study some of the extra structure
present when studying abelian varieties mod p. Possible topics will
include:

- Honda-Tate theory (i.e. classification of abelian varieties
over finite fields up to isogeny)
- Serre-Tate theory (i.e. deformation theory of ordinary abelian
varieties)
- Newton polygons and stratifications of the moduli spaces of abelian
varieties