For more information about this meeting, contact Jason Morton.

Title: | On the geometry of tensor network states |

Seminar: | Applied Algebra and Network Theory Seminar |

Speaker: | Ke Ye, Texas A&M |

Abstract: |

We answer a question of L. Grasedyck that arose in quantum information theory,
showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor networks states corresponding to trees and loops. Grasedyck’s question has a surprising connection to the area of Geometric Complexity Theory, in that the result is equivalent to the statement that the boundary of the Mulmuley-Sohoni type variety associated to matrix multiplication is strictly larger than
the projections of matrix multiplication (and re-expressions of matrix multiplication and its projections after changes of bases). Tensor Network States are also related to graphical models in algebraic statistics. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 01 / 25 / 2012 |

Time: | 02:30pm - 03:20pm |