Speaker: Gage Hoefer, Dartmouth College

Date: September 29, 2026

Abstract: Over the past few decades, significant attention has been devoted to the study of noncommutative geometry with truncated spectral data. One approach to this- introduced by Alain Connes and Walter van Suijlekom- emphasizes operator systems over operator algebras. These objects are well-suited for modeling compact quantum metric spaces, a generalization of classical metric spaces put forward by Marc Rieffel and which have natural connections to operator algebras and quantum groups. With this framework, we may rigorously pose questions about convergence of quantum metric spaces with an analogue of the Gromov-Hausdorff distance for classical compact metric spaces. While previous work has often been focused on finite-dimensional truncations of a space, a more general principle of convolving against kernels (and a connection with Berezin quantization) suggests another approach to approximating a compact quantum metric space— this is the perspective we take up. In this talk, I will give a gentle introduction to operator systems, compact quantum groups, and their actions on operator algebras. Motivated by the smoothing of functions through convolution against well-behaved measures, I show how the analogue of such an operation in the setting of compact quantum groups can be used to construct families of compact quantum metric spaces which converge in a suitable sense to a target space. Examples which stress connections to the classical theory will be provided.

This talk is based on joint work with Trevor Camper and Dimitrios Giannakis.