Abstract:
Given an action of a group G on a space M, it is a classical question to
compute the invariants.  I will introduce a technique to compute the ring of
invariants by considering groupoids equivalent to the groupoid arising from
the action of G on M or equivalently by considering different presentations of
the stack [M/G].  I will apply this technique to explain both the
Gelfand-MacPherson correspondence and the Gale Transform as well as offer
generalizations.  I will also discuss applications to the moduli space of
ordered points in P^1 and the Kontsevich space M_0(P^1,2) in characteristic 2.