A collection of survey papers on the 50th anniversary of the institute.

The implications of Unification Thought applied to modern science solving many of the problems that have arisen.

This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad overview on actual and future research directions in this fascinating and rapidly expanding area.

Mathematical physics has become, in recent years, an inde pendent and important branch of science. It is being increasingly recognized that a better knowledge and a more effective channeling of modern mathematics is of great value in solving the problems of pure and applied sciences, and in recognizing the general unifying principles in science. Conversely, mathematical developments are greatly influenced by new physical concepts and ideas. In the last century there were very close links between mathematics and theo retical physics. It must be taken as an encouraging sign that today, after a long communication gap, mathematicians and physicists have common interests and can talk to each other. There is an unmistak able trend of rapprochement when both groups turn towards the com mon source of their science-Nature. To this end the meetings and conferences addres sed to mathematicians and phYSicists and the publication of the studies collected in this Volume are based on lec tures presented at the NATO Advanced Study Institute on Mathemati cal Physics held in Istanbul in August 1970. They contain review papers and didactic material as well as original results. Some of the studies will be helpful for physicists to learn the language and methods of modern mathematical analysis-others for mathematicians to learn physics. All subjects are among the most interesting re search areas of mathematical physics.

The Conference on Statistical Physics, High Energy, Condensed Matter and Mathematical Physics was held in honor of Professor Chen-Ning Yang's 85th birthday in Singapore in Oct-Nov 2007. The conference paid tribute to the breadth and depth of Professor Yang's achievements in physics and science education since he received his Nobel Prize in Physics fifty years ago. This unique and invaluable birthday volume is a collection of the presentations made at the conference by many eminent scientists who had worked closely with him or who have been influenced to some extent by his work. It covers a wide range of topics, ranging from statistical to high energy to mathematical physics.

This volume contains the proceedings of the Arizona School of Analysis and Mathematical Physics, held from March 5–9, 2018, at the University of Arizona, Tucson, Arizona. A main goal of this school was to introduce graduate students and postdocs to exciting topics of current research that are both influenced by physical intuition and require the use of cutting-edge mathematics. The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics. Two works investigate spectral gaps of quantum spin systems. Specifically, Abdul-Rahman, Lemm, Lucia, Nachtergaele, and Young consider decorated AKLT models, and Lemm demonstrates a finite-size criterion for D D-dimensional models. Bachmann, De Roeck, and Fraas summarize a recent proof of the adiabatic theorem, while Bachmann, Bols, De Roeck, and Fraas discuss linear response for interacting Hall insulators. Models on general graphs are the topic of the articles by Fischbacher, on higher spin XXZ, and by Latushkin and Sukhtaiev, on an index theorem for Schrödinger operators. Probabilistic applications are the focus of the articles by DeMuse and Yin, on exponential random graphs, by Saenz, on KPZ universality, and by Stolz, on disordered quantum spin chains. In all, the diversity represented here is a testament to the enthusiasm this rich field of mathematical physics generates.

Christina Jungnickel and Russell McCormmach have created in these two volumes a panoramic history of German theoretical physics. Bridging social, institutional, and intellectual history, they chronicle the work of the researchers who, from the first years of the nineteenth century, strove for an intellectual mastery of nature. Volume 1 opens with an account of physics in Germany at the beginning of the nineteenth century and of German physicists' reception of foreign mathematical and experimental work. Jungnickel and McCormmach follow G. S. Ohm, Wilhelm Weber, Franz Neumann, and others as these scientists work out the new possibilities for physics, introduce student laboratories and instruction in mathematical physics, organize societies and journals, and establish and advance major theories of classical physics. Before the end of the nineteenth century, German physics and its offspring, theoretical physics, had acquired nearly their present organizational forms. The foundations of the classical picture of the physical world had been securely laid, preparing the way for the developments that are the subject of volume 2.

Quantum physics provides the concepts and their mathematical formalization that lend themselves to describe important properties of biological networks topology, such as vulnerability to external stress and their dynamic response to changing physiological conditions. A theory of networks enhanced with mathematical concepts and tools of quantum physics opens a new area of biological physics, the one of systems biological physics.

Mathematical physics has made enormous strides over the past few decades, with the emergence of many new disciplines and with revolutionary advances in old disciplines. One of the especially interesting features is the link between developments in mathematical physics and in pure mathematics. Many of the exciting advances in mathematics owe their origin to mathematical physics — superstring theory, for example, has led to remarkable progress in geometry — while very pure mathematics, such as number theory, has found unexpected applications.The beginning of a new millennium is an appropriate time to survey the present state of the field and look forward to likely advances in the future. In this book, leading experts give personal views on their subjects and on the wider field of mathematical physics. The topics covered range widely over the whole field, from quantum field theory to turbulence, from the classical three-body problem to non-equilibrium statistical mechanics.