## (Log) Twisted Curves and moduli of stable maps

Martin Olsson, IAS/U.T. Austin

Abstract:
Abramovich and Vistoli introduced the notion of a twisted curve
in order to define compact moduli spaces of stable maps into a
Deligne--Mumford stack. In this talk I will discuss an equivalence
between this notion of twisted curve and a new notion of log twisted
curve, which is a nodal curve equipped with some logarithmic data (in the
sense of Fontaine and Illusie). Then I will discuss various applications
of this equivalence, and in particular explain how it can be combined with
a general theory of Hom--stacks to give simple proofs of the existence and
boundedness of the moduli of twisted stable maps into a Deligne--Mumford
stack.