Cédric Villani - Böcker

“This man could plainly do for mathematics what Brian Cox has done for physics” — Sunday TimesHow does a genius see the world? Where and how does inspiration strike?Cédric Villani takes us on a mesmerising adventure as he wrestles with the Boltzmann equation – a new theorem that will eventually win him the most coveted prize in mathematics and a place in the mathematical history books. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness.His story is one of courage and partnership, doubt and anxiety, elation and despair. Of ordinary family life blurring with the abstract world of mathematical physics, of theories and equations that haunt your dreams and seeking the elusive inspiration found only in a locked, darkened room.Blending science with history, biography with myth, Villani conjures up an inimitable cast: the omnipresent Einstein, mad genius Kurt Godel, and Villani’s personal hero, John Nash.Step inside the magical world of Cédric Villani…

In the words of the great poet Senghor, Cedric Villani makes the bold claim that Mathematics is the Poetry of Science. Perhaps paradoxical to some, both disciplines are concerned with describing the world around us, understanding its parts, and using this knowledge to create something profound. World-renowned mathematician and Fields Medallist Cedric Villani explores this analogy in this engaging and intelligent text, and shows how mathematics, one of the world's few universal languages, holds deep similarities to the literary genre. A great lover of poetry, he insists that the two are intrinsically linked in their aim of both tackling the complexities of our reality as well as distancing us from it so that we may better appreciate its beauty.In a more light-hearted and concise approach than his more theoretical academic works, this book represents one of Villani's attempts to communicate his love of mathematics to a wider audience, drawing daring parallels between two universes that meet in their aspiration of the sublime.

The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.

This book provides an overview of the role of AI in medicine and, more generally, of issues at the intersection of mathematics, informatics, and medicine. Its goal is to provide clear, objective, and reasonable information on the issues covered, avoiding any fantasies that the topic “AI” might evoke.

This book provides an overview of the role of AI in medicine and, more generally, of issues at the intersection of mathematics, informatics, and medicine. Its goal is to provide clear, objective, and reasonable information on the issues covered, avoiding any fantasies that the topic “AI” might evoke.

This volume includes expanded lecture notes from the Mathemata Summer School and Festum Pi 2024 conference, held in Chania, Crete, in July 2024. The lectures focus on advanced analysis techniques for tackling problems in mathematical physics, covering recent advancements in the study of phase transitions, interacting particle systems, kinetic theory, qualitative properties of degenerate Vlasov equations, optimal transport methods for parabolic diffusion equations, and Ricci flow. This volume serves as a valuable resource for researchers exploring modern developments in mathematical analysis. Additionally, it includes two lectures on music theory, reflecting the spirit of Festum Pi 2024.

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view.The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. PhD students or researchers can read the entire book without any prior knowledge of the field.

Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level.During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.

This volume collects the notes of the CIME course "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon).They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rate-independent evolution problems.The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields.

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. PhD students or researchers can read the entire book without any prior knowledge of the field.

This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment.  The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.