Road intersections represent the primary bottleneck in transportation systems and connected autonomous vehicles (CAVs) have the potential to aleviate the problem through communication and coordination. As such, this work proposes a novel framework where, accounting for CAVs' location uncertainty, an intersection manager (IM) controls CAVs approaching a road crossing so as to maximize the number of admitted vehicles, while ensuring a guaranteed (tunable) level of safety. To fully exploit the communication links among the IM and the CAVs, several features are included in the proposed framework: (i) periodic re-optimizations of the CAVs' applied controls; (ii) periodic re-ordering of the intersection crossing sequence; and (iii) event-based control and ordering optimizations to achieve the best possible trade-off between complexity and performance. The proposed framework is able to improve both the number of admitted CAVs to the intersection and the CAVs' average speeds as compared to relevant state-of-the-art solutions. Importantly, when event-triggering is applied, most of the benefits introduced by periodic optimizations are retained, while at the same time the number of re-optimizations required are reduced by 47.6% (34.18%) during average (heavy) traffic conditions.