This three-volume work contains articles collected on the occasion of Alexander Grothendieck's sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world's greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck's own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category...
This three-volume work contains articles collected on the occasion of Alexander Grothendieck's sixtieth birthday and originally published in 1990. ...
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material ...
The main goal of the book is to present a proof of the following. Thurston's Hyperbolization Theorem ("The Big Monster"). Suppose that M is a compact atoroidal Haken 3-manifold that has zero Euler characteristic. Then the interior of M admits a complete hyperbolic metric of finite volume. This theorem establishes a strong link between the geometry and topology 3 of 3-manifolds and the algebra of discrete subgroups of Isom(JH ). It completely changed the landscape of 3-dimensional topology and theory of Kleinian groups. Further, it allowed one to prove things that were beyond the reach of the...
The main goal of the book is to present a proof of the following. Thurston's Hyperbolization Theorem ("The Big Monster"). Suppose that M is a compact ...
This is a greatly revised and expanded version of the book Cardinal fu- tionsonBooleanalgebras, Birkh] auser1990.Knownmistakesinthatbookhave beencorrected, andmanyoftheproblemsstatedtherehavesolutionsinthepresent treatment. At the same time, many new problems are formulated here; some as development of the solved problems from the earlier work, but most as a result of more careful study of the notions. The book is supposed to be self-contained, and for that reason many classical results are included. ForhelponthisbookIwishtothankE.K.vanDouwen, K.Grant, L. Heindorf, I. Juh asz, S. Koppelberg,...
This is a greatly revised and expanded version of the book Cardinal fu- tionsonBooleanalgebras, Birkh] auser1990.Knownmistakesinthatbookhave beencorre...
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs (-expanders-). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one...
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar t...
Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume...
Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding fi...
This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the...
This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axio...
Automorphic forms on the upper half plane have been studied for a long time. Most attention has gone to the holomorphic automorphic forms, with numerous applications to number theory. Maass, 34], started a systematic study of real analytic automorphic forms. He extended Hecke's relation between automorphic forms and Dirichlet series to real analytic automorphic forms. The names Selberg and Roelcke are connected to the spectral theory of real analytic automorphic forms, see, e. g., 50], 51]. This culminates in the trace formula of Selberg, see, e. g., Hejhal, 21]....
Automorphic forms on the upper half plane have been studied for a long time. Most attention has gone to the holomorphic automorphic forms, with numero...
