Modeling–Analysis–Optimization of discrete, continuous, and stochastic systems

Optimization problems accompany us all the time in our every-day life. For example supermarkets guarantee the supply by optimizing the route of transportation of their goods, electricity providers optimize the supply with electricity, and highways are built in a way such that cars produce as little noise as possible. For this, discrete, stochastic, which means influenced by randomness, and continuous mathematical models are used, which need to be analyzed. In order to solve such problems, it is often essential to have a multi-perspective view and combine the knowledge of several mathematical sub-disciplines to create synergies. In crossing these borders lies a great innovative potential. It is the aim of the doc.funds doctoral school and its nine professors from the Departments of Mathematics and Statistics at the University of Klagenfurt to provide PhD students with the mathematical knowledge necessary for understanding and solving challenging mathematical questions, coming from optimization problems in every-day life.

Over its five-year funding period from 2020 to 2025, the FWF doc.funds doctoral school Modeling - Analysis - Optimization of discrete, continuous, and stochastic systems delivered structured doctoral training in mathematics with an international orientation and strong research mobility. In total, 15 doctoral positions were supported through the programme. By the end of the funding period, 11 doctoral candidates successfully completed their PhD degrees, among them a recipient of the national Award of Excellence 2023 for their dissertation. Nine of the graduates are women, reflecting the programme's strong contribution to promoting gender balance in mathematics. Four doctoral candidates entered the programme at a later stage and are now continuing their research under thematically aligned funding arrangements. A central element of the doctoral school was its multi-faceted and internationally oriented supervision model, ensuring strong academic guidance while also supporting broader professional development. Each doctoral candidate received support from two supervisors and benefited from an international mentor acting as a research collaborator, together with a local mentor serving as a professional role model. International mobility was a core component of the programme. All doctoral candidates spent funded research periods abroad, ranging from short-term visits to longer research stays, to strengthen their scientific profiles and build international collaboration. As a result, the programme helped integrate doctoral research into international networks and supported collaborative projects across partner institutions. Beyond individual research projects, the doctoral school placed strong emphasis on scientific exchange and community building. A doctoral retreat was held in 2021 to foster communication and collaboration across different mathematical subdisciplines. The doctoral school ran two summer schools with international lecturers and participants: a summer school on aspects of optimization in 2022 and a summer school on inverse problems in 2023. The programme also offered dedicated professional development workshops to support career readiness. Graduates of the programme have pursued careers in academia and industry both nationally and internationally, demonstrating the broad range of opportunities supported by the training.