This volume contains the proceedings of the conference A Panorama on Singular Varieties, celebrating the 70th birthday of Lê Dũng Tráng, held from February 7–10, 2017, at the University of Seville, IMUS, Seville, Spain. The articles cover a wide range of topics in the study of singularities and should be of great value to graduate students and research faculty who have a basic background in the theory of singularities.

This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg–Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert–Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(–Walker) and Seiberg–Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg–Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.

This book introduces a 'Big History' perspective to understand the acceleration of social, technological and economic trends towards a near-term singularity, marking a radical turning point in the evolution of our planet. It traces the emergence of accelerating innovation rates through global history and highlights major historical transformations throughout the evolution of life, humans, and civilization. The authors pursue an interdisciplinary approach, also drawing on concepts from physics and evolutionary biology, to offer potential models of the underlying mechanisms driving this acceleration, along with potential clues on how it might progress. The contributions gathered here are divided into five parts, the first of which studies historical mega-trends in relation to a variety of aspects including technology, population, energy, and information. The second part is dedicated to a variety of models that can help understand the potential mechanisms, and support extrapolation. In turn, the third part explores various potential future scenarios, along with the paths and decisions that are required. The fourth part presents philosophical perspectives on the potential deeper meaning and implications of the trend towards singularity, while the fifth and last part discusses the implications of the Search for Extraterrestrial Intelligence (SETI). Given its scope, the book will appeal to scholars from various disciplines interested in historical trends, technological change and evolutionary processes.

The debut novel from a exciting new voice in SF—about what happens after ninety percent of humanity leaves Earth There is an artificial ring around the Earth and it is empty after the Singularity. Either all the millions of inhabitants are dead, or they have been transformed into energy beings beyond human perception. Earth's population was reduced by ninety percent. Human civilization on Earth is now recovering from this trauma and even has a vigorous space program. Apollo Papadopulos is in training to become the captain of the starship Consensus. Apollo is a unique individual in that he/she/it is not an individual at all, but five separate teenagers who form a new entity. Strom, Meda, Quant, Manuel, and Moira are a pod, as these kinds of personalities are called, genetically engineered to work as one and to be able to communicate non-verbally. As a rare quintet, much relies on the successful training of Apollo, but as more accidents occur, the pod members struggle just to survive. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

The aim of these essays is to disentangle us from the opposition between universalism and relativism in which so many of the debates in recent contemporary philosophy have been caught. This volume shows that what is in fact returning in these discussions and maneuvering them into a pre-set course is the very ambiguity, `the subject', which they seek to repress.

This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS

### Discover the Future with "The Singularity Conundrum"! Unlock the mysteries of tomorrow with "The Singularity Conundrum," an illuminating eBook that dives deep into the realms of artificial intelligence and its potential to reshape our world. This comprehensive guide takes readers on a transformative journey facing the ever-evolving landscape of AI, offering unparalleled insights into the dawn of a technological singularity. ### Inside "The Singularity Conundrum" #### **The Concept of the Singularity** Explore the origins, key theorists, and controversial debates that have shaped the singularity narrative. Understand through historical and contemporary lenses what the singularity means for the future. #### **Current State of Artificial Intelligence** From everyday applications to cutting-edge developments, get a clear picture of where AI stands today. Compare weak AI to strong AI, and discover the underpinnings of machine learning and neural networks. #### **Potential AI Advancements Leading to the Singularity** Investigate groundbreaking technologies such as quantum computing, advanced robotics, and natural language processing that are propelling us toward the singularity. #### **Ethical Considerations** Delve into critical discussions about AI’s decision-making power, privacy issues, and algorithmic bias. Understand the ethical landscape surrounding AI advancements. #### **The Role of Government and Policy** Learn about current legislative measures, international cooperation, and the future regulatory needs essential to guide AI development ethically and effectively. #### **Economic Impacts** Analyze job automation, shifts in labor markets, AI investment trends, and strategies for wealth redistribution in an AI-driven economy. #### **Human Enhancement and AI** Uncover the future of human augmentation with technologies like brain-computer interfaces and genetic engineering. Explore the possibilities for enhancing human cognition. #### **Sociocultural Implications** Consider the profound changes AI will bring to social interactions, education systems, and cultural norms. #### **Technological Singularities in History** Relate past technological revolutions, such as the Agricultural and Industrial Revolutions, to our current trajectory toward singularity. #### **Predicting the Timeline to Singularity** Review roadmaps, key milestones, and the uncertainties as predicted by leading AI experts. #### **AI and Human Identity** Reflect on how AI might redefine intelligence and reshape the human-AI relationship, delving into deep philosophical questions. #### **Preparing for a Post-Singularity World** Envision educational reforms, lifelong learning, and community resilience in a singularity-aged society. #### **AI in Creativity and the Arts** See how AI is transforming art and music, redefining creativity in the process. #### **AI in Healthcare and Space Exploration** Discover AI’s profound influence on diagnostic tools, personalized medicine, robotic surgeries, and revolutionary space missions. #### **Case Studies in AI Development** Examine real-world examples of AI innovation from leading organizations like OpenAI, DeepMind, and IBM Watson. #### **Public Perception and Media Influence** Consider how AI is portrayed in popular culture, addressing common fears, misconceptions, and the role of educational media. #### **AI and the Future of Work** Navigate new remote work environments, AI in HR, and the emergence of novel job categories. #### **Social Dynamics in an AI-Driven Society** Explore the changing family structures, community building in the digital age, and the balance between online and offline interactions. #### **AI Governance and Decentralization** Look into algorithmic transparency, blockchain integration, and citizen involvement in AI development. #### **The Role of Open Source in AI** Experience the power of collaborative innovation through case studies and the benefits and challenges of open-source AI. Embark on this essential exploration of a future intertwined with artificial intelligence. "The Singularity Conundrum" offers a vital roadmap to understanding and preparing for the profound changes ahead. Don't miss this crucial read—prepare yourself for the future today!

In Search of Singularity introduces a new “compairative” methodology that seeks to understand how the interplay of paired texts creates meaning in new, transcultural contexts. Bringing the worlds of contemporary Polish and Chinese poetry since 1989 into conversation with one another, Joanna Krenz applies the concept of singularity to draw out resonances and intersections between these two discourses and shows how they have responded to intertwined historical and political trajectories and a new reality beyond the human. Drawing on developments such as AI poetry and ecopoetry, Krenz makes the case for a fresh approach to comparative poetry studies that takes into account new forms of poetic expression and probes into alternative grammars of understanding.