The project aims to bridge fundamental PDE theory, mathematical modelling, and modern data-science approaches in order to extract mechanistic insights from high-dimensional biological data.
Building on a long-standing collaboration in the theory of partial differential equations (PDEs) with Prof. Piotr Gwiazda (IMPAN/ICM, University of Warsaw), the project integrates mathematical modelling with statistical inference through collaboration with Prof. Błażej Miasojedow (MIMUW, University of Warsaw). A new research direction has recently been established together with Prof. Paweł Dłotko (TRAILS – Trustworthy Artificial Intelligence for Life Sciences Centre, University of Gdańsk), focusing on topological methods for analysing single-cell transcriptomic data and inferring cell-state transitions, which in turn inform the structure and selection of mechanistic models.
The project combines PDE theory, functional analysis, statistical learning, and topological data analysis to develop model-based approaches for extracting biological mechanisms from high-dimensional single-cell data. Applications focus on neural stem cell dynamics and differentiation processes studied in collaboration with Prof. Ana Martin-Villalba and her group at the German Cancer Research Center (DKFZ) in Heidelberg as part of a joint ERC Synergy Grant. The collaboration also involves early-career researchers from all partner institutions and aims to strengthen long-term scientific links between mathematics, data science, and cell biology.
The scientific strength of the project lies in the complementary expertise of the team, a proven record of collaboration, and its alignment with current challenges in cell biology. Methodologically, the project seeks to extend existing mathematical theory by incorporating geometric and topological features into the functional-analytic framework, exploring model dynamics, and developing computational tools for model-based data analysis. These approaches will be integrated with experimental studies aimed at deciphering the role of heterogeneity and regulatory mechanisms in stem-cell systems.
Period abroad: June, September 2026
“I applied for the 4EU+ Visiting Professorships programme for several reasons. First, it allows me to extend and deepen my long-term collaboration with colleagues in Warsaw, especially with Prof. Piotr Gwiazda from the Institute of Mathematics of the Polish Academy of Sciences (IMPAN) and the University of Warsaw. It also enables me to develop new collaborations with Prof. Błażej Miasojedow and Prof. Paweł Dłotko in the area of statistical data analysis.
The Visiting Professorships programme is a great opportunity to change one’s academic environment, establish new collaborations, and focus on interesting research topics. It is also an attractive initiative due to its relatively low level of bureaucracy, which makes it easier to initiate and develop joint projects.”