A Luna etale slice theorem for algebraic stacks
-- Jarod Alper, December 11, 2015

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Quotient stacks are a distinguished class of algebraic stacks which
provide key intuition for studying the geometry of general algebraic
stacks.  It has long been believed that certain algebraic stacks are
in some sense "locally" quotient stacks. In this talk, we will prove
that this expectation holds by providing a description of the etale
local structure of algebraic stacks near points with linearly
reductive stabilizer.  We will then discuss a number of striking
applications of this result.  This is joint work with Jack Hall and
David Rydh.