For more information about this meeting, contact Karl Schwede, Robert Vaughan, Mihran Papikian, Ae Ja Yee.

Title: | A geometric application of tensor networks |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Shamil Shakirov, UC Berkeley |

Abstract: |

An important geometric property of a surface is the volume
that it bounds. This volume is invariant under SL(n) transformations;
for quadratic surfaces (ellipsoids) it is simply the inverse square
root of the determinant. I will tell how, more generally, for
algebraic surfaces of higher degree, the bounded volume is a function
of the elementary SL(n) invariants of the surface -- the tensor
networks. I will demonstrate on examples that this function is
typically of hypergeometric type, derive the differential equations
that it satisfies, and argue that its singularities are determined by
the discriminant of the surface. This last property is especially
interesting and could have further applications in statistical
physics, which I will mention if time permits. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 11 / 21 / 2013 |

Time: | 11:15am - 12:05pm |