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A Concise Introduction to Algebraic Varieties
A Concise Introduction to Algebraic Varieties is designed for a one-term introductory course on algebraic varieties over an algebraically closed field, and it provides a solid basis for a course on schemes and cohomology or on specialized topics, such as toric varieties and moduli spaces of curves. The book balances generality and accessibility by presenting local and global concepts, such as nonsingularity, normality, and completeness using the language of atlases, an approach that is most commonly associated with differential topology. The book concludes with a discussion of the Riemann-Roch theorem, the Brill-Noether theorem, and applications. The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic point-set topology. A course in graduate algebra is helpful but not required. The book includes appendices presenting useful background in complex analytic topology and commutative algebra and provides plentiful examples and exercises that help build intuition and familiarity with algebraic varieties.
Innovative Techniques and Applications of Entity Resolution
Entity resolution is an essential tool in processing and analyzing data in order to draw precise conclusions from the information being presented. Further research in entity resolution is necessary to help promote information quality and improved data reporting in multidisciplinary fields requiring accurate data representation. Innovative Techniques and Applications of Entity Resolution draws upon interdisciplinary research on tools, techniques, and applications of entity resolution. This research work provides a detailed analysis of entity resolution applied to various types of data as well as appropriate techniques and applications and is appropriately designed for students, researchers, information professionals, and system developers.
Tropical Truth(s)
The 18 contributions to this volume deal with a variety of 'tropes', such as metaphor, metonymy, synecdoche, irony, euphemism, antonomasia and hyperbole. Using various approaches or paradigms the authors aim to find answers to the crucial epistemological questions, namely whether and to what extent utterances containing tropes can be said to be true or false.
Surveys on Recent Developments in Algebraic Geometry
The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
