Mauro Carfora - Böcker

Our existence as living beings - thinking, feeling, acting - is an extraordinary thing: this book provides a scientifically based account of the entirety of factors that lead to our existence. The text begins with the physical foundations of our existence, examining the cosmological context of the vast expanding and evolving universe, enabling the existence of the Sun and the Earth. It goes on to summarise the underlying physics and chemistry, explaining behaviour on an atomic and molecular level, and considers the nature of biological emergence, arguing that all complex systems are modular hierarchical structures, allowing function to emerge at every level, and both upward and downward interactions occur between emergent levels. The book then goes on to examine fundamental processes such as metabolism, dealing with material and energy needs, and homeostasis, stabilising the system against perturbing influences. At the molecular level, this is all enabled by change of shape of macromolecules, and the text looks at how we come into being by a combination of natural selection and developmental processes, which interact with each other and with physiology. Finally, the book discusses the brain and mind, emphasizing the interaction of rationality and emotions, and examining the nature of mental causation and free will. It then delves into existence on a societal level, showing how social institutions having causal powers, and arguing that society can be understood as a homeostatic feedback system relating welfare to social, economic, political, and legal interactions. All social outcomes are determined crucially by our values, the nature of which can be represented by a spectrum of values ranging from very destructive and selfish to very constructive and generous. The final chapter discusses whether meaning exists in the universe, providing evidence that the answer is yes, arguing for moral realism and the existence of a series of abstract possibility spaces that form the deep structure of the cosmos.

This book discusses key conceptual aspects and explores the connection between triangulated manifolds and quantum physics, using a set of case studies ranging from moduli space theory to quantum computing to provide an accessible introduction to this topic.Research on polyhedral manifolds often reveals unexpected connections between very distinct aspects of mathematics and physics. In particular, triangulated manifolds play an important role in settings such as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, critical phenomena and complex systems. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is also often a consequence of an underlying structure that naturally calls into play non-trivial aspects of representation theory, complex analysis and topology in a way that makes the basic geometric structures ofthe physical interactions involved clear.This second edition further emphasizes the essential role that triangulations play in modern mathematical physics, with a new and highly detailed chapter on the geometry of the dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory. This connection is treated in depth, pinpointing both the mathematical and physical aspects of the perturbative embedding of the Ricci flow in the renormalization group flow of non-linear sigma models. The geometry of the dilaton field is discussed from a novel standpoint by using polyhedral manifolds and Riemannian metric measure spaces, emphasizing their role in connecting non-linear sigma models’ effective action to Perelman’s energy-functional. No other published account of this matter is so detailed and informative.This new edition also features an expanded appendix on Riemannian geometry, and a rich set of new illustrations to help the reader grasp the more difficult points of the theory. The book offers a valuable guide for all mathematicians and theoretical physicists working in the field of quantum geometry and its applications.

This volume contains lectures on recent advances in the theory of integrable systems and quantum groups. It introduces the reader to attractive areas of current research.

This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold.