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# Dynamics on the moduli space of flat structures

## Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015

May 15, 2015 (11:20 AM PDT - 12:10 PM PDT)
Speaker(s): Maryam Mirzakhani (Stanford University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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Abstract

The moduli space of holomorphic one-forms on a closed surface of genus $g$ has a natural piecewise linear structure and carries an action of GL(2,R). One can investigate the geometry and dynamics of an individual flat surface by studying its orbit under this linear group action. I will discuss several open problems regarding the properties of these orbit closures. This talk is based on joint work with Alex Eskin, Amir Mohammadi and Alex Wright.

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