There are many open problems in the study of complex systems which call for new insights and new mathematical methods of modelling. In the workshop the recent exciting developments in $p$-adic methods for the modelling of complex systems in biology, physics and cosmology will be addressed. This project is clearly interdisciplinary and it
requires the presence of scientists from different disciplines.
Concerning biological applications, problems of genetics, as well as problems posed by the dynamics of complex macromolecules (in particular, proteins), and the phenomenon of presence of quantum effects in photosynthesis will be particular discussed, together with promising approaches to spin glasses and diffusion based on $p$-adic analysis.
In cosmology there are successful phenomenological approaches to the parameters of inflation scenario but a more fundamental approach is needed. Recently non local cosmological models based on $p$-adic string theory have been proposed which in principle could provide a solution of the problem posed by the large values of the inflation.
These and other problems in biology, physics and cosmology are in fact deeply related because they have common intrinsic hierarchical structures which can be mathematically modelled by using ultrametric analysis and, in particular, $p$-adic numbers. The innovativity and the great promise of the research to be discussed in the workshop rely on the application of the above mentioned new mathematical tools which are very appropriate for the modelling of complex systems with hierarchical structure.
Albeverio Sergio A
Khrennikov Andrei Yur'evich
Kozyrev Sergei Vladimirovich
Shelkovich Vladimir Mikhailovich
Volovich Igor Vasil'evich
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow