I'm currently working on a project entitled "Positivity and monotonicity methods in infinite-dimensional systems theory". This is funded by the DFG and is a joint project with Felix Schwenninger (Twente) and Jochen Glück (Wuppertal). The first year of the project (2023-2024) will be spent at Twente and in the second year (2024-2025), it will continue in Wuppertal.
Project summary. Positive systems arise naturally in many applications such as population, diffusion, and transport models. Positivity constraints impose limitations on the system which simplifies the analysis of the qualitative behaviour of the system. Whereas the positivity of finite-dimensional systems has been relatively well studied, there is a lack of a general theoretical framework for the study of positive systems in infinite dimensions. This project aims to bridge this gap via three different yet interlinked objectives.