The Fell topology and the modular Gromov-Hausdorff propinquity (Jiahui Yu, Pomona College)

Given a unital AF (approximately finite-dimensional) algebra A equipped with a faithful tracial state, we equip each (norm-closed two-sided) ideal of A with a metrized quantum vector bundle structure, when canonically viewed as a module over A, in the sense of Latrémolière using previous work of Aguilar and Latrémolière. Moreover, we show that convergence of ideals in the Fell topology implies convergence of the associated metrized quantum vector bundles in the modular Gromov-Hausdorff propinquity of Latrémolière. In a similar vein but requiring a different approach, given a compact metric space (X,d), we equip each ideal of C(X) with a metrized quantum vector bundle structure, and show that convergence in the Fell topology implies convergence in the modular Gromov-Hausdorff propinquity. (This is joint work with Konrad Aguilar).