| Abstract |
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We will discuss the dynamics of isoperiodic foliations of strata of
holomorphic 1-forms (or translation surfaces). Leaves of this
foliation are navigated by varying a holomorphic 1-form without
changing its integrals along closed loops. Roughly speaking, this is
done by moving the zeros of the 1-form relative to each other. In the
generic stratum, the dynamics of this foliation are well-understood
due to a close connection with homogeneous dynamics. In this talk, I
will discuss a classification of leaf closures for this foliation in
all strata, outside of a high-codimension subvariety, in the spirit of
Ratner's orbit closure theorem.
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For future talks or to be added to the mailing list: www.math.uh.edu/dynamics.