Heritage, World Heritage, and the Future by
An exploration of heritage practice in Turkey at the intersection of academia, policy, and practice. The papers published in this volume were among those presented at the 14th International ANAMED Annual Symposium (IAAS), held at Istanbul's Koç University Research Center for Anatolian Civilizations in 2019. Bringing together archaeologists and heritage professionals from diverse backgrounds engaged in the conservation of archaeological and natural sites, the symposium focused on topics of heritage conservation and development in Turkey, with a particular focus on World Heritage Sites. The papers in this volume explore the conservation and future of archaeological and natural heritage, including but not limited to the World Heritage Convention and its application in Turkey, site conservation and financing of conservation work, community engagement during archaeological research, and public perceptions of archaeology. Providing reflection on and critical assessment of their own work, the authors discuss both achievements and problems to create a clearer picture of what works and what does not work in certain conditions.
Intermittent Convex Integration for the 3D Euler Equations by
A new threshold for the existence of weak solutions to the incompressible Euler equations To gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L^2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates.
Comparison Principles for General Potential Theories and PDEs by
An examination of the symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories In recent years, there has evolved a symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories. This book examines important aspects of this story. One main purpose is to prove comparison principles for nonlinear potential theories in Euclidian spaces straightforwardly from duality and monotonicity under the weakest possible notion of ellipticity. The book also shows how to deduce comparison principles for nonlinear differential operators, by marrying these two points of view, under the correspondence principle. The authors explain that comparison principles are fundamental in both contexts, since they imply uniqueness for the Dirichlet problem. When combined with appropriate boundary geometries, yielding suitable barrier functions, they also give existence by Perron's method. There are many opportunities for cross-fertilization and synergy. In potential theory, one is given a constraint set of 2-jets that determines its subharmonic functions. The constraint set also determines a family of compatible differential operators. Because there are many such operators, potential theory strengthens and simplifies the operator theory. Conversely, the set of operators associated with the constraint can influence the potential theory.
Modern Trends in Algebra and Representation Theory by
Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.
Algebraic Combinatorics and the Monster Group by
Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
Maurer-Cartan Methods in Deformation Theory by
Covering an exceptional range of topics, this text provides a unique overview of the Maurer--Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
Digital Immigrants and Media Integration by
In Digital Immigrants and Media Integration: The Smartphone Is the Synthesizer, Sally J. McMillan draws insights from the lived experience of digital immigrants who are Baby Boomers and who grew up without digital mobile technologies and have transitioned to become smartphone users. McMillan traces key points in media evolution that shaped the communication tools that digital immigrants use today, demonstrating that continued incremental change has led to a shift in focus from media types to media interfaces, with smartphones becoming ubiquitous and indispensable - the smartphone, she posits, is now firmly tied to identity. Although the telegraph was the first medium to allow the message to arrive before the messenger and initiated the transition from "cool" to "hot" media, it is the smartphone that has fully synthesized communication forms and functions into a single digital and mobile device. Through collecting and analyzing these personal and public histories, McMillan finds that digital immigrants continue to seek a balance between value and ease, and between breadth and depth of communication. Scholars of communication, media ecology, and technology will find this book of particular interest.
Gooey Media by
The Graphic User Interface, or GUI, is the adhesive centre of today's screen entertainment web. From films and television to apps and videogames, it holds together a multitude of media and shapes the way they are accessed, organised, created, consumed, and manipulated. However, it does not do so without leaving viscous traces, and Gooey Media: Screen Entertainment and the Graphic User Interface examines this residue and its consequences, revealing how the GUI exerts a powerful influence on contemporary media. Focusing on aesthetics and adopting a media agnostic approach, Jones explores cinema, streaming platforms, television, user-generated content, videogames, apps, virtual reality, VFX, design software, and more in order to show how they cross-pollinate with one another and with our desktop interfaces. The result is a new approach for analysing convergent media in the digital era.
