Research interests
My mathematical research interests are
Biomathematics and modelling:
- Mechanical models for cell dynamics; agent-based models
- Developmental biology (epithelial-to-mesenchymal transitions)
- Actin-myosin dynamics
- Elasticity theory
Numerics:
- Geometric numerical methods (symplectic methods, finite element exterior calculus)
- Coupled systems and inequality constraints (differential inclusions, position-based dynamics)
Analysis:
- Non-smooth dynamical systems (differential inclusions on uniformly prox-regular sets)
- Mean-field limits (in particular with constraints)
Current projects
The results shown in this section are work in progress.
Cell migration model for plithotaxis
Jun 2021 – present
Goal: Development of an agent-based cell migration model for plithotaxis.
Jun 2021 – present
Goal: Development of an agent-based cell migration model for plithotaxis.
First-order position-based dynamics
Oct 2020 – present
Goal: Numerical analysis of a very simple, but equally fast and stable numerical method from computer graphics.
Oct 2020 – present
Goal: Numerical analysis of a very simple, but equally fast and stable numerical method from computer graphics.
Mechanical modelling of epithelial-to-mesenchymal transitions
Oct 2019 – present
Goal: Modelling of different EMT scenarios to study their effect on metastasis. (Read more...)
Oct 2019 – present
Goal: Modelling of different EMT scenarios to study their effect on metastasis. (Read more...)
Past projects
Mean-field limit for constrained particles
Mar 2018 – Mar 2022
Goal: Proof of the mean-field limit for an abstraction of a muscle tissue model.
Mar 2018 – Mar 2022
Goal: Proof of the mean-field limit for an abstraction of a muscle tissue model.
Sara Merino-Aceituno and me exploring an interactive simulation of our cell migration model for plithotaxis. This was part of an outreach activity that I developed for the “Long night of Science” in Vienna.