The research period will focus on an understanding of collective behaviors in particle and biological systems with emphasis on the mesoscopic approach. The activity will consist mainly in advanced lectures on Probability and Biology, main topics being on Patterns, Interaction, and Kinetics. It will also include several advanced seminars in Biology and lectureson mathematical problems raised by Biology. The research period will give the opportunity to Ph.D. and Post Doc students to learn advanced subjects and address their researches. Secondly it will allow researchers from different areas to meet and discuss the frontiers of these subjects.
Patterns formation in Nature. Self-organization, interaction, taxonomy of patterns (metrics), geometry and kinetics of patterns, connection to Biology. To a first approximation biological system can be envisaged as an open interacting particle physical systems and tools from statistical physics, and other sciences of complexity, have been recently successfully applied. Qualitative features of collective behavior include pattern formation, transitions between order and disorder, the study of fluctuations, phase transition, long-range correlations, scaling, symmetry breaking, ... Methods based on autonomous agents are also extensively used, e.g., in the study of swarming of insects, flocking of birds, schooling of fish, motion of bacteria. The research period at the Centro E. De Giorgi will focus on the study of formalizable structures, i.e., consistent mathematical approaches that reflect the pattern formation behavior. We will both be interested in methods for recognizing patterns and in the formalization of the pattern concept in terms of a pattern theory. Models, predictions and control. The biologist seeks for an understanding of the complexity of the observable statistics at the macroscopic level in terms of simple rules. He tries, through experiments, to isolate patterns in the biological systems in order to make predictions. The research period will present several key concepts together with concrete examples from Nature with emphasis on the combination between theory and experiment. Modeling tools and methodologies will be presented. Moreover, recent domains of engineering research involving bio-inspired artefacts for control will be presented (lures, bio-inpired robots, ...). Mathematical problems raised by Biology. During the whole research period mathematical problems raising from Biology will be enhanced in advanced lectures and seminars. We will also include future research perspectives.