PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact 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