Come hear about the research carried out by Oki Amalia and Filippo Testa during the PhD at the UT in two different talks!

"Scheduling surgeries with different priorities in dedicated operating room capacities"by Oki Amalia

In hospitals, patients who need treatment or surgery are often categorized based on their urgency levels, each with its own due date. In our work, we consider surgeries of two urgency levels: urgent surgery, which must start within 6 hours, and semi-urgent surgery, which must start within 24 hours. Scheduling urgent and semi-urgent patients is non-trivial, as patients have multiple priority levels and thus different due date targets. The scheduler continuously balances between reserving capacity for urgent patients that is potentially left idle and meeting the due dates for all patients. We present two policies to schedule urgent and semi-urgent patients in the dedicated operating room (OR) capacity: last-minute scheduling and near-online scheduling. Under last-minute scheduling, the scheduler assigns capacity to the waiting patients just before the start of the time slot in which the patient will be treated. Under near-online scheduling, the scheduler assigns a future time slot to the patient shortly after the patient's arrival. We developed a Markov decision process (MDP) for both scheduling policies. Further, we also propose two heuristics based on the policy that is easily applied by hospitals. In the first heuristic, we use all available capacity to schedule patients from the highest urgency level. In the second heuristic, we allow reserving capacity to anticipate urgent patient arrivals in the subsequent time slot. For the time-varying patient arrivals, we use nonstationary MDP, where we evaluate the performance of the optimal policies using discrete event simulation and compare it to the policies from the heuristics. We demonstrate the usefulness of our method by applying it to the case of our partnering hospital.

"Contact points between analysis and geometry: the Poincaré-Hopf theorem" by Filippo Testa

Given an object, it is often possible to establish a connection between its topological and geometrical properties (its shape) and the analytical properties of functions defined on it.

Many results in this regard have been achieved, deeply intertwining the fields of geometry and analysis. This talk will introduce the Poincaré-Hopf theorem, which connects the shape of a manifold with the zeroes of vector fields defined on it, while also containing a basic introduction to the language of differential geometry. We will also go over some of its implications, like the hairy ball theorem.