Analysis seminar
Speaker: Sushil Singla, University of Regina, Canada
Host: Santanu Dey
Title: Representations of noncommutative cubes and prisms
Time, day and date: 3:45:00 PM - 4:45:00 PM, Tuesday, August 04
Venue: Ramanujan Hall
Abstract: In this talk, I will describe certain noncommutative realizations of three classical geometric objects: cubes, polydiscs, and prisms. I will establish the connection of representations of discrete groups with the noncommutative extreme points of the noncommutative state space of the operator systems generated by the canonical unitaries that correspond to the generators of the group. Using this connection, I will be shedding light on the noncommutative geometry of noncommutative dcubes and k-prisms via the representations of the operator system determined by the canonical generators of the free product of two cyclic groups of order 2 and k, or d cyclic groups of order 2. By way of the duality of the categories NCConv and OpSys of noncommutative convex sets and operator systems, respectively, I will also establish an analysis of tensor products of the operator system under consideration.
Finally, I will apply classical dilation theorems of Halmos and Mirman to give a complete description of the maximal noncommutative triangular prism in terms of joint unitary dilations. This is joint work with D. Farenick, R. Maleki, and S. Medina Varela, and has been accepted for publication in J. Noncommut. Geom. The preprint of the article is available on Arxiv:2601.16902.