For more information about this meeting, contact Svetlana Katok, Stephanie Zerby, Anatole Katok, Federico Rodriguez Hertz.

Title: | Equidistribution of stretching translates of curves on homogeneous spaces |

Seminar: | Center for Dynamics and Geometry Colloquium |

Speaker: | Nimish Shah, Ohio State University |

Abstract: |

We consider a finite piece C of an analytic curve on a minimal expanding (abelian) horospherical subgroup of G=SL(n,R) associated to a certain diagonal element g in G. We consider the subgroup action of G on a finite volume homogeneous space X, and consider the trajectory of C from some point x in X. We want to understand algebraic conditions on C which ensure that in the limit, the translates of the curve Cx by g^n get equidistributed in the (homogeneous) closure of the G-orbit of x as 𝑛→∞. In this talk we describe some recent joint work with Lei Yang on this problem.
Such results have applications to metric properties of Diophantine approximation; for example, to show non-improvability of Dirichlet’s approximation on curves in the space of matrices. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 03 / 29 / 2016 |

Time: | 02:30pm - 03:29pm |