Mathematical optimization is a formal language that allows expressing an optimization problem as a mathematical model. In particular, the decisions to be made are represented by variables and technical/strategic constraints by inequalities, while a function of the variables is optimized. In this seminar, we present how such a powerful tool can be applied in the urban air mobility context to solve the tactical deconfliction (TD) problem. TD is an online problem aimed at identifying and fixing potential conflict between each pair of aircraft passing through the same air space. While TD is a well-known problem in air traffic management, its specialization to the urban air mobility case has some peculiarities. Our mathematical model is one of the first attempts to fully formalize such a problem and to propose a solution to it. We test our method on three different scenarios, where the following sources of conflict are generated: i. standard conflicts due to delay w.r.t. the original planning; ii. a priority flight that has to be integrated into the original planning; iii. an intruder flight. The tested instances are generated to be realistic. We compare our approach to the standard local deconfliction and the fairness-oriented version.