Crossing the borders of physics and biology
New mathematical descriptions of natural phenomena

The development of new mathematical and computational models of biological processes has a tremendous impact on our understanding of the world as well as the possibility of influencing selected processes. Models developed in collaboration with biologists and physicians have repeatedly enabled the verification of existing and emerging research hypotheses as well as facilitated the design of new experiments. Recognition by the scientific community that the description of complex biological processes with mathematical language has tremendous importance for our better understanding of these processes is a breakthrough for the development of biomedical sciences. Notably, the benefits are mutual. Mathematical modelling has a genuine chance to contribute to the development of mathematics, being a flywheel in areas such as numerical analysis (e.g. numerical solving of parabolic-hyperbolic problems, free boundary problems), qualitative analysis of partial differential equations (e.g. travelling wave or bifurcation analysis), asymptotic and multi-scale analysis (e.g. homogenisation), useful for the correct derivation of macroscopic models taking into account microscopic data. Often, the construction and analysis of a new model require the use of novel mathematical methods. Below we list three main scientific focuses of the current programme. Each of them is the subject of one of the three main events planned within the programme, which we describe in detail further.

January 2024 – December 2024

• 1. Conference:
  The Cahn-Hilliard equation – recent advances and new challenges
  21-26 of April 2023, European Centre for Geological Education in Chęciny
• 2. Workshop:
  Challenging problems arising from the mathematical description of natural phenomena – part I
• 3. Workshop:
  Challenging problems arising from the mathematical description of natural phenomena – part II
• 4. Scientific visits:
  Temporary employment of visiting professors and visits of scientific guests

• Jose Antonio Carrillo (University of Oxford),
• Piotr Gwiazda (Institute of Mathematics, Polish Academy of Sciences),
• Jakub Skrzeczkowski (University of Oxford & University of Warsaw),
• Zuzanna Szymańska (ICM, University of Warsaw),

• Piotr Gwiazda (Institute of Mathematics, Polish Academy of Sciences),
• Jakub Skrzeczkowski (University of Oxford & University of Warsaw),
• Zuzanna Szymańska (ICM, University of Warsaw),
• Katarzyna Kulczycka-Mierzejewska (ICM, University of Warsaw)

crossing@icm.edu.pl