报告题目： Patterns emerging from spatially heterogeneous backgrounds---a panorama in Turing's sight
In the seminal paper "The chemical basis of morphogenesis" Alan Turing explained the mechanism of spontaneous formation of nontrivial spatial structures (patterns) as the result of "Diffusion-Driven-Instability", which says reaction between two chemicals with different diffusion rates can destabilize spatially uniform states. In this talk we try to generalize his idea and show that reaction-diffusion mechanism can overcome the given spatial heterogeneity and create new spatial structures. We hope this new viewpoint can explain various stages of pattern formation in biological systems.
Professor Izumi Takagi is a well-known specialist in nonlinear PDEs. His areas of interest are Pattern Formation in Reaction-Diffusion Systems, Geometric Variational Problems in Biology.
He was trained as an analyst in Mathematical Institute, Tohoku University (Japan) and received a DrSci in Mathematics in 1985. He was Professor of applied mathematics in Tohoku University for twenty years and now he is Professor of Institute for Mathematical Sciences in Renmin University.
One of his main achievements is the discovery of a “point-condensation phenomenon” in reaction-diffusion equations, which was done in the joint project with Professor Wei-Ming Ni (Minneapolis, USA) and triggered the research on various concentration phenomena observed in solutions of nonlinear PDEs. Recently he has been collaborating with mathematical biologists led by Professor Dr. Marciniak-Czochra in Heidelberg University, Germany.