Search results for ""Author William Fulton""

There are few more powerful questions than, “Where are you from” or “Where do you live?” People feel intensely connected to cities as places and to other people who feel that same connection. In order to understand place – and understand human settlements generally – it is important to understand that places are not created by accident. They are created in order to further a political or economic agenda. Better cities emerge when the people who shape them think more broadly and consciously about the places they are creating. In Place and Prosperity: How Cities Help Us to Connect and Innovate, urban planning expert William Fulton takes an engaging look at the process by which these decisions about places are made, how cities are engines of prosperity, and how place and prosperity are deeply intertwined. Fulton has been writing about cities over his forty-year career that includes working as a journalist, professor, mayor, planning director, and the director of an urban think tank in one of America’s great cities. Place and Prosperity is a curated collection of his writings with new and updated selections and framing material. Though the essays in Place and Prosperity are in some ways personal, drawing on Fulton’s experience in learning and writing about cities, their primary purpose is to show how these two ideas – place and prosperity – lie at the heart of what a city is and, by extension, what our society is all about. Fulton shows how, over time, a successful place creates enduring economic assets that don’t go away and lay the groundwork for prosperity in the future. But for urbanism to succeed, all of us have to participate in making cities great places for everybody. Because cities, imposing though they may be as physical environments, don’t work without us. Cities are resilient. They’ve been buffeted over the decades by White flight, decay, urban renewal, unequal investment, increasingly extreme weather events, and now the worst pandemic in a century, and they’re still going strong. Fulton shows that at their best, cities not only inspire and uplift us, but they make our daily life more convenient, more fulfilling – and more prosperous.

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Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.

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Geechi Suede and Sonny Cheeba are Camp Lo. These two emcees from the Bronx, NY entered the American hip hop scene with an insider slang that bewildered listeners as they radiated the look of a bygone era of black culture. In 1996, they collaborated with producer Ski and a host of other contributors to create Uptown Saturday Night, featuring the seminal single “Luchini (a.k.a. This is It).” While other 1990s rappers referred to 1970s Blaxploitation culture, Camp Lo were self-described “time travelers” who weaved the slang and style of a soulful past into state-of-the-art lyrical flows. Uptown Saturday Night is a tapestry of 1970s black popular culture and 1990s New York City hip hop. This volume will detail how the album’s fantastic world of “Coolie High” reflected classic films like Cooley High and the Sidney Poitier film from which the album’s title is derived, and promoted vintage slang and fashion. The book features new interviews with Camp Lo, producer Ski, Trugoy the Dove from De La Soul, Ish from Digable Planets, and others, and offers musical and cultural analyses that detail the development of the album and its essential contributions to a post-soul aesthetic.

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Equivariant cohomology has become an indispensable tool in algebraic geometry and in related areas including representation theory, combinatorial and enumerative geometry, and algebraic combinatorics. This text introduces the main ideas of the subject for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics. The first six chapters cover the basics: definitions via finite-dimensional approximation spaces, computations in projective space, and the localization theorem. The rest of the text focuses on examples – toric varieties, Grassmannians, and homogeneous spaces – along with applications to Schubert calculus and degeneracy loci. Prerequisites are kept to a minimum, so that one-semester graduate-level courses in algebraic geometry and topology should be sufficient preparation. Featuring numerous exercises, examples, and material that has not previously appeared in textbook form, this book will be a must-have reference and resource for both students and researchers for years to come.

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