Events for 06/18/2020 from all calendars

Seminar in Random Tensors

Time: 2:00PM - 3:00PM

Location: zoom

Speaker: Guillaume Aubrun, Lyon 1

Title: Entangleability of cones

Abstract: Given two finite-dimensional cones, one can naturally define their minimal and maximal tensor products. We show that both coincide if and only if one of the cones is simplex-based, as was conjectured by Barker (1976). Our proof involves a mix of convex geometry, elementary algebraic topology, and computations inspired by quantum information theory (arXiv:1911.09663, joint with Ludovico Lami, Carlos Palazuelos and Martin Plavala).

Noncommutative Geometry Seminar

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Javier Alejandro Chavez-Dominguez, University of Oklahoma

Title: Asymptotic dimension and coarse embeddings in the quantum setting

Abstract: We generalize the notions of asymptotic dimension and coarse embeddings from metric spaces to quantum metric spaces in the sense of Kuperberg and Weaver. We show that quantum asymptotic dimension behaves well with respect to metric quotients, direct sums, and quantum coarse embeddings. Moreover, we prove that a quantum metric space that equi-coarsely contains a sequence of reflexive quantum expanders must have infinite asymptotic dimension. This is done by proving a vertex-isoperimetric inequality for quantum expanders, based upon a previously known edge-isoperimetric one due to Temme, Kastoryano, Ruskai, Wolf, and Verstraete. Joint work with Andrew Swift.

Seminar on Banach and Metric Space Geometry

Time: 4:00PM - 5:00PM

Location: online

Speaker: Alejandro Chavez-Domınguez, University of Oklahoma

Title: Asymptotic dimension and coarse embeddings in the quantum setting

Abstract: We generalize the notions of asymptotic dimension and coarse embeddings from metric spaces to quantum metric spaces in the sense of Kuperberg and Weaver. We show that quantum asymptotic dimension behaves well with respect to metric quotients, direct sums, and quantum coarse embeddings. Moreover, we prove that a quantum metric space that equi-coarsely contains a sequence of reflexive quantum expanders must have infinite asymptotic dimension. This is done by proving a vertex-isoperimetric inequality for quantum expanders, based upon a previously known edge-isoperimetric one due to Temme, Kastoryano, Ruskai, Wolf, and Verstraete. Joint work with Andrew Swift.