Fritz, Marvin

Partial differential equations are a key mathematical tool for describing complex processes in nature, medicine and engineering – from fluid flows and mechanical interactions to biological growth. In my research, I develop and investigate models for current societal challenges, with a particular focus on mathematical oncology: that is, the modelling of tumour growth, tumour invasion and the effects of treatment. I am interested in how real biological and physical mechanisms – such as non-local cell-cell interactions, mechanical stresses, vascular networks or random influences – can be captured mathematically. A second focus is on the question of whether these models are mathematically well-defined, that is, whether solutions exist, are unique and react stably to changes in the input data; this is the basis for ensuring that subsequent simulations are reliable. Finally, I develop numerical methods that preserve key structures of the models – such as energy and mass conservation – even in the discrete domain, thereby enabling stable, efficient and realistic calculations. 

• Numerical analysis and structure-preserving discretisation of partial differential equations
• Well-posedness and long-term behaviour of nonlinear evolutionary PDEs
• Stochastic and non-local partial differential equations
• Mathematical modelling of tumour growth, therapy and angiogenesis
• Control and stabilisation of PDE systems
• Applications in biomedicine, biophysics and nonlinear acoustics
   

• 2012–2015 Bachelor’s degree in Mathematics, Technical University of Munich
• 2015–2017 Master’s degree in Mathematics, Technical University of Munich
• 2018 Visiting Researcher at the Institute for Computational Engineering and Sciences, University of Texas at Austin
• 2018–2022 Research Assistant and PhD candidate at the Chair of Numerical Mathematics, Technical University of Munich
• 2022–2026 Research Scientist at the Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences
• 2023–2026 University Assistant, Johannes Kepler University Linz
• since June 2026 Tenure-track professorship at the Faculty of Mathematics, University of Vienna