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Abstract:
We will begin by giving an elementary introduction to the
GL(2,R) action on the Hodge bundle (sometimes called Teichmuller
dynamics), after which we will give a survey of some of new developments
in this field. This will include severe restrictions on the structure of
orbit closures echoing Ratner's Theorems on homogeneous spaces, the
surprising discovery by Moller and Filip that orbit closures can be
defined purely in terms of algebraic geometry, and new and surprising
examples of sub-varieties of the Hodge bundle which provide
counterexamples to a conjecture of Mirzakhani. The talk will include
joint work with Alex Eskin, Simion Filip, Curtis McMullen,
Maryam Mirzakhani, and Ronen Mukamel.
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