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This work aims to foster the interdisciplinary dialogue between mathematicians and socio-economic scientists. Interaction among scholars and practitioners traditionally coming from different research areas is necessary more than ever in order to better understand many real-world problems we face today. On the one hand, mathematicians need economists and social scientists to better address the methodologies they design in a more realistic way; on the other hand, economists and social scientists need to be aware of sound mathematical modelling tools in order to understand and, ultimately, solve the complex problems they encounter in their research. With this goal in mind, this work is designed to take into account a multidisciplinary approach that will encourage the transfer of knowledge, ideas, and methodology from one discipline to the other. In particular, the work has three main themes: Demystifying and unravelling complex systems; Introducing models of individual behaviours in the social and economic sciences; Modelling socio-economic sciences as complex living systems. Specific tools examined in the work include a recently developed modelling approach using stochastic game theory within the framework of statistical mechanics and progressing up to modeling Darwinian evolution. Special attention is also devoted to social network theory as a fundamental instrument for the understanding of socio-economic systems.
Über den Autor / die Autorin
Bouchra Aylaj is an Associate Professor with Habilitation in mathematics at University of Hassan II of Casablanca, Faculty Ain Chock, Morocco. She started her career in 2006 when she was called to develop a research program on mathematical modelling in biology. Her scientific activity has been focused on the following topics: scientific computing and control for risk analysis and analytical and computational problems in epidemiology. Subsequently, she moved her scientific interests to the modeling and related safety problems focused on social behaviors in human crowds.
Nicola Bellomo is a distinguished professor at the University of Granada and Professor Emeritus at the Polytechnic University of Torino. He started his career in 1980 when he was called to cover the chair of mathematical physics and applied mathematics due to his scientific achievements on the mathematical theory of the Boltzmann equation and of stochastic differential equations. Subsequently, he moved his scientificinterests to the study of living systems, becoming one of the pioneers of the development of active particles methods to the modeling of large systems of self-propelled interacting entities. He is author of two books published by Birkhauser devoted to this topic. In 2009, he delivered the prestigious Shank Lecture on the modeling of immune competition, and was awarded the "Third Level Honor" in 2016 for scientific merits by the President of the Italian Republic.
Livio Gibelli is a Lecturer in Mechanical Engineering at the University of Edinburgh. He received his Ph.D. in applied mathematics from the Politecnico di Milano and, prior to the current position, he worked as Research Fellow at the University of Warwick, Politecnico di Milano, Politecnico di Torino, and University of British Columbia. His main research interests include non-equilibrium multiphase fluid flows, the continuum description of slightly rarefied gases, the numerical methods for solving kinetic equations,and the modeling of crowd dynamics.
Damian Knopoff is a chemical engineer and mathematician, holding a Ph.D. in Mathematics from Cordoba National University. Currently, he is an Associate Researcher at the Argentinian Scientific and Technical Research Council. His main research fields include nonlinear dynamical systems and numerical methods for differential equations with applications to the modeling and simulation of complex living systems, including biological phenomena, socio-economic systems, and crowd dynamics.
Zusammenfassung
This work aims to foster the interdisciplinary dialogue between mathematicians and socio-economic scientists. Interaction among scholars and practitioners traditionally coming from different research areas is necessary more than ever in order to better understand many real-world problems we face today. On the one hand, mathematicians need economists and social scientists to better address the methodologies they design in a more realistic way; on the other hand, economists and social scientists need to be aware of sound mathematical modelling tools in order to understand and, ultimately, solve the complex problems they encounter in their research. With this goal in mind, this work is designed to take into account a multidisciplinary approach that will encourage the transfer of knowledge, ideas, and methodology from one discipline to the other. In particular, the work has three main themes: Demystifying and unravelling complex systems; Introducing models of individual behaviours in the social and economic sciences; Modelling socio-economic sciences as complex living systems. Specific tools examined in the work include a recently developed modelling approach using stochastic game theory within the framework of statistical mechanics and progressing up to modeling Darwinian evolution. Special attention is also devoted to social network theory as a fundamental instrument for the understanding of socio-economic systems.
