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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. 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. 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...

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent. More than 10 years after a first meeting between number theorists and physicists at the Centre de Physique des Houches, a second two-week event focused on the broader interface of number theory, geometry, and physics. This book collects the material presented at this meeting.

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent. More than 10 years after a first meeting between number theorists and physicists at the Centre de Physique des Houches, a second two-week event focused on the broader interface of number theory, geometry, and physics. This book collects the material presented at this meeting.

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent...

This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cedric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cedric Villani s popular success proves once...