The research of the Biomathematics group is guided by the principle of moving constantly from rigorous mathematics to applications and back. Members of this group collaborate with specialists in medicine (tumor growth modeling, immune reaction, and cancer therapy; Forys), cell biology (gene expression and regulation, signaling pathways; Miekisz), hydrology (structure of zooplankton; Wrzosek), evolutionary biology and social sciences (existence of altruistic behavior in the Darwinian word of the survival of the fittest within the framework of evolutionary game theory; Platkowski).
Time delays, stochastic fluctuations, and population structure present in such systems provide inspirations for studying general time-delay differential equations (Bodnar, Forys, Piotrowska), combined effects of time delays and stochasticity in dynamical systems (Miekisz), stochastic processes and mathematical connections between micro, mezzo, and macro levels in description of natural phenomena, and scaling limits (Lachowicz), partial differential equations (Peradzynski, Szopa), differential equations with the age and size structure (Wrzosek), evolutionary game theory (Miekisz, Platkowski), and dynamical games with continuous spaces of players (Wiszniewska-Matyszkiel).
The Biomathematics team lead by Rudnicki plans to study structured population models which appear in physiology and genomics. They intend to obtain new results concerning asymptotic behaviour of such models as stability, periodicity, invariant measures, and chaos. Developed mathematical ideas and techniques will be, in turn, applied in various models of natural and social sciences. The additional value of the Biomathematics group is that some of its members have both mathematical and physical educational background, have worked in both areas, and are using now techniques of statistical physics in exploring biological and social systems.