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Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and provide a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail. ... Read more

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Chapters: Alexander Grothendieck, Paul Cohen, Atle Selberg, René Thom, Edward Witten, Enrico Bombieri, Alain Connes, John Milnor, William Thurston, Michael Atiyah, Lars Ahlfors, Stephen Smale, Heisuke Hironaka, Vladimir Voevodsky, Laurent Lafforgue, Maxim Kontsevich, Richard Borcherds, Grigori Perelman, Shing-Tung Yau, David Mumford, Terence Tao, Lars Hörmander, Jean-Pierre Serre, Grigory Margulis, Timothy Gowers, Simon Donaldson, Alan Baker, Laurent Schwartz, John G. Thompson, Vladimir Drinfel'd, Sergei Novikov, Pierre Deligne, Kunihiko Kodaira, Charles Fefferman, Michael Freedman, Daniel Quillen, Vaughan Jones, Wendelin Werner, Andrei Okounkov, Pierre-Louis Lions, Jesse Douglas, Jean Bourgain, Curtis T. Mcmullen, Efim Zelmanov, Gerd Faltings, Shigefumi Mori, Jean-Christophe Yoccoz, Klaus Roth. Source: Wikipedia. Pages: 229. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Sir Michael Francis Atiyah, OM, FRS, FRSE (born 22 April 1929) is a British mathematician, and one of the most influential mathematicians of the twentieth century. He grew up in Sudan and Egypt, and spent most of his academic life at Oxford, Cambridge, and the Institute for Advanced Study in Princeton. He has been President of the Royal Society (19901995), Master of Trinity College, Cambridge (19901997), Chancellor of the University of Leicester (19952005), and President of the Royal Society of Edinburgh (20052008). He is currently retired and an honorary professor at the University of Edinburgh. He has had many mathematical collaborations, in particular with Raoul Bott, Friedrich Hirzebruch and Isadore Singer, and his students include Graeme Segal, Nigel Hitchin and Simon Donaldson. With Hirzebruch he founded topological K-theory, a major tool in algebraic topology, that describes the ways in which high dimensional space...More: http://booksllc.net/?id=20698 ... Read more