Mathematical Understanding of Patterns

in the Life Sciences


March 18 27, 2003



This workshop was held at the Lorentz Center from March 18th to March 27th, 2003. It was organized by Danielle Hilhorst (Orsay), Hiroshi Matano (Tokyo), Masayasu Mimura (Hiroshima), and Mark Peletier (Amsterdam). The number of registered participants reached 68, of which a large part came from France, Japan, and the Netherlands, but there were also participants from Australia, Belgium, Hungary, Israel, Italy, Germany, the Czech Republic, U.K., and U.S.A.


The main purpose of this workshop was the understanding of the formation of complex phenomena in biology and chemistry with a multidisciplinary approach, incorporating ideas and insight both from mathematics and from the life sciences; the speakers were mathematicians, biologists, theoretical physicists, and chemists. The workshop revolved around various topics in the mathematical study of formation and dynamics of complex patterns, which can be observed in areas such as morphogenesis, bacterial growth, immune systems, ecological systems, and chemical reactions. The topics of the lectures included in particular travelling fronts in homogeneous and heterogeneous media, singular limits and interface dynamics, blow-up and extinction phenomena, and numerical methods.


Among the very positive aspects of this workshop is the fact that indeed people from theoretical biology, theoretical physics and mathematics have come together and been able to interact on a number of problems, such as:


       Pattern formation due to reproduction and movement of bacterial cells (M. Howard, P. Maini, M. Matsushita, M. Mimura, C. Muratov, H. Zaag)

       Invasions in heterogeneous media (H. Berestycki, H. Matano, N. Shigesada)

       Population dynamics (N. Dancer, O. Diekmann, M. Langlais, N. Shigesada)

       The modelling of problems arising in medicine such as tissue penetration, tumor growth, cellular rythms (X. Chen, J. Demongeot, A. Goldbeter, J. King)

       Problems arising in chemistry (J. Boissonade, C.J. van Duijn, A. Doelman, H. Fraaije, F. Otto)


Quite naturally many new ideas have come up out of those interactions and most of them will very probably lead to substantial scientific collaborations.


As a conclusion, this conference was well focused with its multidisciplinary approach of complex patterns. Mathematicians learned a lot from listening to biologists, physicists, and chemists who in turn enjoyed the discussions with mathematicians working towards a rigorous understanding of the biological phenomena. During and after the conference, we received very positive response from many of the participants. Surely a lot of them will keep meeting each other and interacting in the coming years.


D. Hilhorst (University Paris-Sud, France)

H. Matano (University of Tokyo, Japan)

M. Mimura (Hiroshima University, Japan)

M. Peletier (CWI, The Netherlands)