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A Panorama of Singularities by Francisco-Jesús Castro-Jiménez,David Bradley Massey,Bernard Teissier,Meral Tosun Pdf
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.
Introduction to Lipschitz Geometry of Singularities by Walter Neumann,Anne Pichon Pdf
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all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves.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.
$p$-Adic Analysis, Arithmetic and Singularities by Carlos Galindo,Alejandro Melle Hernández,Julio José Moyano-Fernández,Wilson A. Zúñiga-Galindo Pdf
This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications. This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces $p$-adic analysis, the theory of Archimedean, $p$-adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists. This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.
Abelian Varieties and Number Theory by Moshe Jarden,Tony Shaska Pdf
This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.
Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties by Paola Comparin,Eduardo Esteves,Herbert Lange,Sebastián Reyes-Carocca,Rubí E. Rodríguez Pdf
Articles in this volume are based on lectures given at three conferences on Geometry at the Frontier, held at the Universidad de la Frontera, Pucón, Chile in 2016, 2017, and 2018. The papers cover recent developments on the theory of algebraic varieties—in particular, of their automorphism groups and moduli spaces. They will be of interest to anyone working in the area, as well as young mathematicians and students interested in complex and algebraic geometry.
Quaternion Fusion Packets by Michael Aschbacher Pdf
Let p p be a prime and S S a finite p p-group. A p p-fusion system on S S is a category whose objects are the subgroups of S and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory. The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.
Representations of Algebras, Geometry and Physics by Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov Pdf
This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25–30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called “geodesic ghor algebras”, a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of Coxeter groups, powerful new applications of approximable triangulated categories, new results on the heart of a t t-structure, and an introduction to methods of constructive category theory.
p-adic Differential Equations by Kiran S. Kedlaya Pdf
Now in its second edition, this volume provides a uniquely detailed study of $P$-adic differential equations. Assuming only a graduate-level background in number theory, the text builds the theory from first principles all the way to the frontiers of current research, highlighting analogies and links with the classical theory of ordinary differential equations. The author includes many original results which play a key role in the study of $P$-adic geometry, crystalline cohomology, $P$-adic Hodge theory, perfectoid spaces, and algorithms for L-functions of arithmetic varieties. This updated edition contains five new chapters, which revisit the theory of convergence of solutions of $P$-adic differential equations from a more global viewpoint, introducing the Berkovich analytification of the projective line, defining convergence polygons as functions on the projective line, and deriving a global index theorem in terms of the Laplacian of the convergence polygon.
Lie Groups, Number Theory, and Vertex Algebras by Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić Pdf
This volume contains the proceedings of the conference Representation Theory XVI, held from June 25–29, 2019, in Dubrovnik, Croatia. The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three main topics of these articles are Lie theory, number theory, and vertex algebras.
The Mysteries of Paris and London by Richard Maxwell Pdf
In this ambitious and exciting work Richard Maxwell uses nineteenth-century urban fiction--particularly the novels of Victor Hugo and Charles Dickens--to define a genre, the novel of urban mysteries. His title comes from the "mystery mania" that captured both sides of the channel with the runaway success of Eugene Sue's Les mysteres de Paris and G. W. M. Reynold's Mysteries of London. Richard Maxwell argues that within these extravagant but fact-obsessed narratives, the archaic form of allegory became a means for understanding modern cities. The city dwellers' drive to interpret linked the great metropolises with the discourses of literature and art (the primary vehicles of allegory). Dominant among allegorical figures were labyrinths, panoramas, crowds, and paperwork, and it was thought that to understand a figure was to understand the city with which it was linked. Novelists such as Hugo and Dickens had a special flair for using such figures to clarify the nature of the city. Maxwell draws from an array of disciplines, ideas, and contexts. His approach to the nature and evolution of the mysteries genre includes examinations of allegorical theory, journalistic practice, the conventions of scientific inquiry, popular psychiatry, illustration, and modernized wonder tales (such as Victorian adaptations of the Arabian Nights). In The Mysteries of Paris and London Maxwell employs a sweeping vision of the nineteenth century and a formidable grasp of both popular culture and high culture to decode the popular mysteries of the era and to reveal man's evolving consciousness of the city. His style is elegant and lucid. It is a book for anyone curious about the fortunes of the novel in thenineteenth century, the cultural history of that period, particularly in France and England, the relations between art and literature, or the power of the written word to produce and present social knowledge.
Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics by Gert-Martin Greuel,Luis Narváez Macarro,Sebastià Xambó-Descamps Pdf
This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.
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.
A Panoramic View of Riemannian Geometry by Marcel Berger Pdf
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
In this prophetic allegory about artificial intelligence by a renowned figure of twentieth-century Italian literature, a modest university professor becomes involved in a remote and enigmatic project in the middle of the Cold War. At the beginning of Dino Buzzati’s The Singularity, Ermanno Ismani, an unassuming university professor, is summoned by the minister of defense to accept a two-year, top-secret mission at a mysterious research center, isolated from the world among forests, plunging cliffs, and high mountains. What’s he supposed to do there? Not clear. How long will he be there? No saying. Still, Ismani takes the mystifying job and, accompanied by his no-nonsense wife, Elisa, heads to the so-called Experimental Camp of Military Zone 36, wondering whether, in the midst of the Cold War, it’s some sort of nuclear project he’s been assigned to. But no, the colleagues the couple meets on arrival assure them, it’s nothing like that. It’s much, much more powerful. At the center of the research complex is strange, shining, at times murmurous, white wall. Behind it, a deep gorge drops away, full of wires and radio towers and mobile sensors and a host of eccentric structures. A question begins to dawn: Could this be the shape of consciousness itself? And if so, whose? Buzzati's novella of 1960, a pioneering work of Italian science fiction, is published here in a brisk new translation by Anne Milano Appel. In it, Buzzati explores his favorite themes of love and longing while offering a startlingly prescient parable of artificial intelligence.