This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential...
This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields,...
This volume includes papers presented by several speakers at the Geometry and Topology conferences at Harvard University in 2011 and at Lehigh University in 2012. Included are works by Simon Brendle, on the Lagrangian minimal surface equation and related problems; by Sergio Cecotti and Cumrun Vafa, concerning classification of complete N=2 supersymmetric theories in four dimensions; by F. Reese Harvey and H. Blaine Lawson Jr., on existence, uniqueness, and removable singularities for non-linear PDEs in geometry; by Janos Kollar, concerning links of complex analytic singularities; by Claude...
This volume includes papers presented by several speakers at the Geometry and Topology conferences at Harvard University in 2011 and at Lehigh Univers...
This book begins with an historical overview of mathematics at Tsinghua University, describing the life and works of several eminent mathematicians educated there--including Shiing-Shen Chern, Loo-Keng Hua, Chia-Chiao Lin, and Pao-Lu Hsu--and remembering two famous western visitors to Tsinghua, Jacques Hadamard and Norbert Wiener. Furthermore, the book presents some specific plans, and maps a general direction, regarding the role that the Mathematical Sciences Center and the Tsinghua-Sanya International Mathematics Forum will play in mathematics both in China and on the international...
This book begins with an historical overview of mathematics at Tsinghua University, describing the life and works of several eminent mathematicians ed...
The 2012 discovery of the Higgs boson was a sensational triumph-the culmination of a 48-year-long search that put the finishing touches on the so-called "Standard Model" of particle physics. While the celebrations were still underway, researchers in China were making plans to continue the centuries-old quest to identify the fundamental building blocks of nature. More specifically, they began laying the groundwork for a giant accelerator-up to 100 kilometers in circumference-that would transport physics into a previously inaccessible, high-energy realm where a host of new particles, and...
The 2012 discovery of the Higgs boson was a sensational triumph-the culmination of a 48-year-long search that put the finishing touches on the so-call...
This volume consists of articles by speakers at the Conference on Geometry and Topology held at Harvard University in 2014. Included are: Camillo De Lellis, on the size of the singular set of area-minimizing currents; Simon Donaldson, on Kahler-Einstein metrics and algebraic structures on limit spaces; Mark Gross, on theta functions and mirror symmetry; Nigel Hitchin, on Higgs bundles and diffeomorphism groups; Fernando Marques, on topology of the space of cycles and existence of minimal varieties; William Meeks, on constant mean curvature surfaces; Richard Thomas, on the proof of the KKV...
This volume consists of articles by speakers at the Conference on Geometry and Topology held at Harvard University in 2014. Included are: Camillo De L...
Groups and group actions are probably the most central objects in mathematics. Comprising volumes 31, 32, 40 and 41 of the ALM series, the Handbook of Group Actions presents survey articles on the topic of group actions and how they appear in several mathematical contexts. The general subject matter is organized under the following sections: geometry, mapping class groups, knot groups, topology, representation theory, deformation theory, and discrete groups. The various articles deal with both classical material and modern developments. They are written by specialists in their...
Groups and group actions are probably the most central objects in mathematics. Comprising volumes 31, 32, 40 and 41 of the ALM series, the Handbook...
Groups and group actions are probably the most central objects in mathematics. Comprising volumes 31, 32, 40 and 41 of the ALM series, the Handbook of Group Actions presents survey articles on the topic of group actions and how they appear in several mathematical contexts. The general subject matter is organized under the following sections: geometry, mapping class groups, knot groups, topology, representation theory, deformation theory, and discrete groups. The various articles deal with both classical material and modern developments. They are written by specialists in their...
Groups and group actions are probably the most central objects in mathematics. Comprising volumes 31, 32, 40 and 41 of the ALM series, the Handbook...
Geometric flows are non-linear parabolic differential equations which describe the evolution of geometric structures. Inspired by Hamilton's Ricci flow, the field of geometric flows has seen tremendous progress in the past 25 years and yields important applications to geometry, topology, physics, nonlinear analysis, and so on. Of course, the most spectacular development is Hamilton's theory of Ricci flow and its application to three-manifold topology, including the Hamilton-Perelman proof of the Poincare conjecture. This twelfth volume of the annual Surveys in Differential Geometry...
Geometric flows are non-linear parabolic differential equations which describe the evolution of geometric structures. Inspired by Hamilton's Ricci flo...
Deals with the life and work of the great twentieth-century mathematician Shiing-Shen Chern. Included are numerous pages of photographs; an autobiographical article recounting the formation of a mathematical mind and of a great war; historical and personal reminiscences by thirty distinguished mathematicians and physicists including Bott, Griffiths, Lawson, Nirenberg, Singer, Yang, Yau, and others; and a discussion of 100 open problems in geometry. The book is essential for anyone who is interested in understanding Chern and his influence upon twentieth-century century mathematics.
Deals with the life and work of the great twentieth-century mathematician Shiing-Shen Chern. Included are numerous pages of photographs; an autobiogra...