Formality Theory

This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.

Introduction : why is formality so unpopular? -- A redefinition of the concept of formality -- Legal formality and graphical planning languages -- Certainty of the law : reasons, situation-types, analogy, and equilibrium -- The social structure of liquidity : flexibility in markets, states, and organizations / Bruce G. Carruthers, Arthur L. Stinchcombe -- Formalizing rightlessness in immigration law and administration -- Formalizing epistemological stratification of knowledge -- Conclusion : the varieties of formality.

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

What is cultural about vision--or visual about culture? In this ambitious book, Whitney Davis provides new answers to these difficult and important questions by presenting an original framework for understanding visual culture. Grounded in the theoretical traditions of art history, A General Theory of Visual Culture argues that, in a fully consolidated visual culture, artifacts and pictures have been made to be seen in a certain way; what Davis calls "visuality" is the visual perspective from which certain culturally constituted aspects of artifacts and pictures are visible to informed viewers. In this book, Davis provides a systematic analysis of visuality and describes how it comes into being as a historical form of vision. Expansive in scope, A General Theory of Visual Culture draws on art history, aesthetics, the psychology of perception, the philosophy of reference, and vision science, as well as visual-cultural studies in history, sociology, and anthropology. It provides penetrating new definitions of form, style, and iconography, and draws important and sometimes surprising conclusions (for example, that vision does not always attain to visual culture, and that visual culture is not always wholly visible). The book uses examples from a variety of cultural traditions, from prehistory to the twentieth century, to support a theory designed to apply to all human traditions of making artifacts and pictures--that is, to visual culture as a worldwide phenomenon.

For fifty years, The Supreme Court Review has been lauded for providing authoritative discussion of the court's most significant decisions. The Review is an in-depth annual critique of the Supreme Court and its work, keeping up on the forefront of the origins, reforms, and interpretations of American law. Recent volumes have considered such issues as post-9/11 security, the 2000 presidential election, cross-burning, federalism and state sovereignty, failed Supreme Court nominations, and numerous First- and Fourth-Amendment cases.