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The editors of the highly esteemed Journal of Differential Geometry (published by International Press) each year present a new volume of Surveys in Differential Geometry, a collection of original contributions upon a specially chosen topic pertaining to differential geometry and related topics. The series presents an overview of recent trends, while making predictions and suggestions for future research.Each invited contributor is a prominent specialist in the field of algebraic geometry, mathematical physics, or related areas. Contributors to Surveys tend to transcend classical frameworks within their field.Once every three years, Lehigh University and Harvard University, in conjunction with the editors of the JDG, sponsor a conference whose purpose is to survey the general field of differential geometry and related subjects. Speakers at the conference are likewise selected for their prominence in a given field and for their innovative contributions to it. Hence every third volume of Surveys is a publication of those presented talks.The Surveys in Differential Geometry series is a beneficial collection for experts and non-experts alike, and in particular, for those independent of the mainstream of activity in the field of geometry. ... Read more

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Interest in string theory is driven largely by the hope that it will evolve to be the ultimate “Theory of Everything.” Work on string theory has led to advances in many branches of mathematics. This rapidly developing subject is one of the mainstream topics of mathematics in the 21st century.The current volume presents lectures from the important String Theory International Conference held in 2002 in Hangzhou, China. These include talks given by several mathematicians of particular prominence in the field, among them Stephen Hawking and Edward Witten.

Table of contents

Brane New World (Stephen Hawking)
Gauge Theory and Gravity (Edward Witten)
Easing Into QFT (Edward Witten)
Open String Creation by S-brane (Andrew Strominger)
Duality, Gauging and SuperHiggs Effect in String and M-theory (Sergio Ferrara)
Seiberg Witten Curve for the E-String Theory (Tohru Eguchi, Kazuhiro Sakai)
Strings and Noncommutativity (Louise Dolan, Chiara R. Nappi)
Lectures on Two-loop Superstrings (Eric D Hoker, D.H. Phong)
Seiberg-Witten Theory, Symplectic Forms, and Hamiltonian Theory of Solitons (Eric D Hoker, I. Krichever and D.H. Phong)
Quark Mass Hierarchy and Flavor Mixing in Orbifold Models (Zhi-Zhong Xing)
M-theory on Manifolds with Exceptional Holonomy (S. Gukov)
Stability Conditions and the Braid Group (R. P. Thomas)
Some Remarks on Constant Curvature Spaces (Rong-Gen Cai)
Fourier-Mukai Partners and Mirror Symmetry of K3 Surfaces (Shinobu Hosono)
Counting BPS States via Holomorphic Anomaly Equations (Shinobu Hosono)
Symmetries, Matrices, and de Sitter Gravity (Yi-Hong Gao)
Correspondence Principle in a PP-wave Background (Miao Li)
Support of dS/CFT Correspondence from Spacetime Perturbations (Bin Wang)
Quintessence Cosmology in the Brans-Dicke Theory (Chang-Jun Gao, You-Gen Shen)
Entropy in the NUT-Kerr-Newman Black Holes due to an Arbitrary Spin Field (Xian-Hui Ge, You-Gen Shen) ... Read more

Customer Reviews (1)

Part of a simply outstanding series of eight such instructional texts
The need for 'student friendly' instructional texts in the field of mathematics is essential to the continued advancement of science in general, and the technologies upon which our 21st century are based. Now a joint publishing project of the International Press of Boston in cooperation with the Higher Education press of China, undergraduate and graduate level curriculums have access to a simply outstanding series of eight such instructional texts focused on updating the cutting edge of advances in mathematics entitled the 'Advanced Lectures in Mathematics' (ALM). The series consists of "Superstring Theory" comprised of lectures given by leading researchers (including Stephen Hawking and Edward Witten) on the subject; "Asymptotic Theory in Probability and Statistics with Applications" presenting eighteen papers organized into three major sections - limit theorems, statistics and applications, mathematical finance and insurance; "Computational Conformal Geometry" presenting succinct introductions to both its theoretical foundations and the practical applications; "Variational Principles for Discrete Surfaces" surveying among other thematically appropriate subjects, current research in the geometry of polyhedral surfaces with applications to computer graphics; "Fourth International Congress of Chinese Mathematicians" (publication pending); "Geometry, Analysis and Topology of Discrete Groups" featuring fifteen papers focusing on helping graduate students and researchers with the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces; "Handbook of Geometric Analysis No. 1" presenting papers on various aspects of geometric analysis; "Recent Developments in Algebra and Related Areas" comprised of fifteen papers delivered at the International conference on Algebra and Related Areas held at Tsinghua University, Beijing, China in August 2007. Although each volume is available individually, academic library reference collections should acquire the set in its entirety as seminal contributions to the field of higher mathematics for the benefit of the faculties and students they serve.
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From the beginning harmonic maps were studied in connection with the theory of minimal surfaces.

In 1985, the authors presented a series of lectures at the University of California at San Diego on the subject of harmonic maps. Most of these lectures are collected here as Part I. Part I of the book is devoted to harmonic maps defined on Riemann surfaces. Part II was added much more recently, and comprises part of the thesis of the first author, the work of N. Korevaar and the second author, and applications to geometry by the authors. The final chapter is due to J. Jost and the second author. This book presents some of the latest research on this topic from two of the foremost researchers in the field. ... Read more

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Discrete subgroups of Lie groups are foundational objects in modern mathematics and occur naturally in different subjects. This new volume presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory, and topology. Most of the papers are surveys, and the volume is intended to help graduate students and researchers better understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces.

Table of contents

A Survey on Divisible Convex Sets (Yves Benoist)
Distribution of Square Integrable Automorphic Forms on Hilbert Modular Groups (Roelof W. Bruggeman, Roberto J. Miatello)
Scattering Theory for Geometrically Finite Groups (Ulrich Bunke, Martin Olbrich)
Marden's Tameness Conjecture: History and Applications (Richard D. Canary)
Topological Rigidity and Geometric Applications (F. T. Farrell)
The Representation Theory of the Cyclotomic Hecke Algebras of Type G (r, p, n) (Jun Hu )
Harmonic Functions and Compactifications Symmetric Spaces (Adam Korányi)
On Characterizations of Arithmetic Groups among Arbitrary Discrete Subgroups of Lie groups (Enrico Leuzinger)
Ordinary Quiver, AR-quiver and Natural Quiver of an Algebra (Fang Li, Daowei Wen)
Lp-cohomology of Symmetric Spaces (Pierre Pansu)
On the Cohomology of Locally Symmetric Adele Spaces as a Module over the Hecke Algebra (Jürgen Rohlfs)
Cohomology of Discrete Groups and Representation Theory (Birgit Speh)
Some Results on Finite Dimensional Representations of General Linear Lie Superalgebras (Yucai Su)
Twisted Fermat Curves over Totally Real Fields II (Ye Tian)
Bridging the Gap between Incompatible Compactifications of Locally Symmetric Varieties (Steven Zucker) ... Read more

Customer Reviews (1)

Part of a simply outstanding series of eight such instructional texts
The need for 'student friendly' instructional texts in the field of mathematics is essential to the continued advancement of science in general, and the technologies upon which our 21st century are based. Now a joint publishing project of the International Press of Boston in cooperation with the Higher Education press of China, undergraduate and graduate level curriculums have access to a simply outstanding series of eight such instructional texts focused on updating the cutting edge of advances in mathematics entitled the 'Advanced Lectures in Mathematics' (ALM). The series consists of "Superstring Theory" comprised of lectures given by leading researchers (including Stephen Hawking and Edward Witten) on the subject; "Asymptotic Theory in Probability and Statistics with Applications" presenting eighteen papers organized into three major sections - limit theorems, statistics and applications, mathematical finance and insurance; "Computational Conformal Geometry" presenting succinct introductions to both its theoretical foundations and the practical applications; "Variational Principles for Discrete Surfaces" surveying among other thematically appropriate subjects, current research in the geometry of polyhedral surfaces with applications to computer graphics; "Fourth International Congress of Chinese Mathematicians" (publication pending); "Geometry, Analysis and Topology of Discrete Groups" featuring fifteen papers focusing on helping graduate students and researchers with the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces; "Handbook of Geometric Analysis No. 1" presenting papers on various aspects of geometric analysis; "Recent Developments in Algebra and Related Areas" comprised of fifteen papers delivered at the International conference on Algebra and Related Areas held at Tsinghua University, Beijing, China in August 2007. Although each volume is available individually, academic library reference collections should acquire the set in its entirety as seminal contributions to the field of higher mathematics for the benefit of the faculties and students they serve.
... Read more

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These are the proceedings of the joint seminar by M.I.T. and Harvard on the current Developments in mathematics for the year 2002. Established in 1995, this seminar has been continued on the third weekend of November every year. The organizing committee for the seminar consisted of distinguished mathematicians from the mathematics departments of both institutions: Barry Mazur, Wilfried Schmid, and S.T. Yau from Harvard, and David Jerison, TomMrowka, and Richard Stanley from M.I.T. This year, the seminar was dedicated to Prof. Wilfried Schmid and Prof. George Lusztig.

The 2002 speakers included Albert Bressan, Mark Haiman, Richard Rain, Stephan Kudla, Yair Minsky, John Morgan, Leslie Saper, Kari Vilonen, and David Vogan. We trust that these proceedings will be of interest to many mathematicians, and will inspire future developments and research pursuits in mathematics. ... Read more

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Contents

Special Lagrangian fibrations, wall-crossing, and mirror symmetry (Denis Auroux)
Sphere theorems in geometry (Simon Brendle and Richard Schoen)
Geometric Langlands and non-Abelian Hodge theory (Ron Donagi and Tony Pantev)
Developments around positive sectional curvature (Karsten Grove)
Einstein metrics, four-manifolds, and conformally Kähler geometry (Claude LeBrun)
Existence of Faddeev knots (Fengbo Hang, Fanghua Lin, and Yisong Yang)
Milnor K2 and field homomorphisms (Fedor Bogomolov and Yuri Tschinkel)
Arakelov inequalities (Eckart Viehweg)
A survey of Calabi-Yau manifolds (Shing-Tung Yau) ... Read more

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A collection of lectures given by the author and numerous contributors at Tsing Hua University, Taiwan, in 1990-1. Topics covered include: energy in general relativity; existence and convergence of solutions; closed geodesics; and mean curvature evolution. ... Read more

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Cohomology of groups is a fundamental tool in many subjects of modern mathematics. One important generalized cohomology theory is the algebraic K-theory. Indeed, algebraic K-groups of rings are important invariants of the rings and have played important roles in algebra, topology, number theory, etc. This volume consists of expanded lecture notes from a 2007 seminar at Zhejiang University in China, at which several leading experts presented introductions, to and surveys of, many aspects of cohomology of groups and algebraic K-theory, along with their broad applications. Two foundational papers on algebraic K-theory by Daniel Quillen are also included. ... Read more

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Index Theory is one of the most exciting and consequential accomplishments of twentieth-century mathematics. The Founders of Index Theory contemplates the four great mathematicians who developed index theory—Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I.M. Singer—through the eyes of their students, collaborators and colleagues, their friends and family members, and themselves.

In addition to their own essays and correspondence—of historical importance—this volume presents a variety of material of a decidedly personal as well as compelling mathematical nature, written by some of their most notable students and long-time collaborators, including such leading current figures in mathematics and physics as Simon Donaldson, Edward Witten, and S.T. Yau. In these writings, one perceives the expansive influence of their work across various fields of mathematics and into theoretical physics.

At a time when the long and illustrious careers of Atiyah, Hirzebruch, and Singer are being recognized with birthday celebrations at Edinburgh, in Europe, and in Massachusetts, this second edition of Founders of Index Theory remembers the late and much beloved Raoul Bott—in the affectionate words of those three men, as well as family members and long-time friends and colleagues. What emerges is the portrait of a compelling mathematical mind informed by a warm and magnetic personality that was both a joy and inspiration to those who knew him.

This volume includes a generous collection of color and black-and-white photographs—many rarely seen—of the four principal figures together with their family, friends, and colleagues. These include numerous images of Bott dating from his early childhood to his last years at Harvard University.

The Founders of Index Theory, Second Edition is a valuable portrayal of four men who transformed mathematics in a profound manner, and who belong to a class of researchers whose interest and influence transcend the conventional boundaries of mathematical fields.

394 pages, plus 40 pages of color and black-white photographs. ... Read more

Customer Reviews (1)

Features historically significant essays and correspondences
The field of mathematics is a constantly evolving one with new discoveries and theories arising to challenge old methods and assumptions. Such was the case with the creation of 'Index Theory', the cumulative work of Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I.M. Singer. Now in a newly updated and expanded second edition, "The Founders of Index Theory" under the deft and knowledgeable editorship of S. T. Yau draws upon a wide and diverse variety of these four men's students and collaborators, a group which includes such notable and distinguished mathematicians and scientists as Simon Donaldson and Edward Witten. "The Founders of Index Theory" features historically significant essays and correspondences. Of special note for this second edition is the addition information showcasing the role of Raoul Bott drawn from family members and friends. The informed and informative text is enhanced with the inclusion of a large section of photos. A seminal and unique work of meticulous and painstaking scholarship, "The Founders of Index Theory" is especially recommended for academic library American Biography and History of Mathematics reference collections and supplemental reading lists.
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This volume includes lectures on geometry and topology related to the works of the late and venerated S.S. Chern. From the 2005 JDG conference at Harvard University. Larger-format 2008 re-issue with corrected table of contents.

Surveys in Differential Geometry (SDG) is an annual collection of the invaluable talks given at the JDG conference, as well as of remarks from invited scholars. The series presents an overview of recent trends, while making predictions and suggestions for future research. The SDG series is a beneficial collection for experts and non-experts alike, and in particular, for those independent of the mainstream of activity in the field of geometry.

Contents

On the space-time monopole equation (B. Dai, C.-L. Terng & K. Uhlenbeck)
The Erhardt function for symbols (V. Guillemin, S. Sternberg & J. Weitsman)
Recent results on the moduli spaces of Riemann surfaces (K. Liu)
Applications of minimal surfaces to the topology of three-manifolds (W. Meeks)
An integral equation for spacetime curvature in general relativity (V. Moncrief)
Topological strings and their physical applications (A. Nietzke & C. Vafa)
Notes on GIT and symplectic reduction for bundles and varieties (R. P. Thomas)
Perspectives on geometric analysis (S.-T. Yau)
Distributions in algebraic dynamics (S.-W. Zhang) ... Read more

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Classical modular forms on the upper half plane, with respect to the modular group SL(2,Z) and its congruence subgroups, have arisen naturally in number theory, complex analysis, topology, mathematical physics, and many other subjects. The closely related automorphic representations are basic notions in the celebrated Langlands program, which was proposed by Langlands in the late 1960s and has since revolutionized the fields of number theory, arithmetic algebraic geometry, and representation theory. This volume consists of expanded lecture notes from a 2007 international conference in Guangzhou, China, at which several leading experts in number theory presented introductions to, and surveys of, many aspects of automorphic forms and the Langlands program. ... Read more

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The Surveys in Differential Geometry are supplements to the Journal of Differential Geometry, which are published by International Press. They include significant invited papers combining original research and overviews of the most current research in specific areas of interest to the growing Journal of Differential Geometry community. The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers. These supplements are published annually since 1999.

The world-renowned Journal of Differential Geometry sponsors a triannual conference at Harvard University which brings together mathematicians from all over the world. The third conference celebrated the 30th anniversary of the journal, and the 70th birthday of its founding editor, C. C. Hsiung. This volume (Vol.3) of Surveys in Differential Geometry is based on the lectures given during the 3rd conference of Journal of Differential Geometry. ... Read more

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Lectures from the 2009 JDG conference.

Table of Contents

Divisors in the moduli spaces of curves (Enrico Arbarello and Maurizio Cornalba)
Stability phenomena in the topology of moduli spaces (Ralph L. Cohen)
Birational aspects of the geometry of Mg(Gavril Farkas)
The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces (Samuel Grushevsky and Igor Krichever)
Brill-Noether theory (Joe Harris)
GL+2(R)-orbit closures via topological splittings (Pascal Hubert, Erwan Lanneau, and Martin Möller)
Harmonic mappings and moduli spaces of Riemann surfaces (Jürgen Jost and Shing Tung Yau)
Algebraic structures on the topology of moduli spaces of curves and maps (Y.-P. Lee and R. Vakil)
Recent development on the geometry of the Teichmüller and moduli spaces of Riemann surfaces (Kefeng Liu, Xiaofeng Sun, and Shing-Tung Yau)
The universal properties of Teichmüller spaces (Vladimir Markovic and Dragomir Saric)
Geometry of Teichmüller space with the Teichmüller metric (Howard Masur)
GIT constructions of moduli spaces of stable curves and maps (Ian Morrison)
Riemann surfaces, integrable hierarchies, and singularity theory (Yongbin Ruan) ... Read more

Customer Reviews (1)

Deftly compiled and edited
Deftly compiled and edited by the academic editorial team of Lizhen Ji (University of Michigan), Scott A. Wolpert (University of Maryland), and Shing-Tung Yau (Harvard University), "Surveys in Differential Geometry: Volume 14, Geometry of Riemann surfaces and their moduli spaces" is a collection of lectures delivered at the 2009 JDG conference. Comprising this 418-page compendium are Divisors in the moduli spaces of curves (Enrico Arbarello and Maurizio Cornalba); Stability phenomena in the topology of moduli spaces (Ralph L. Cohen); Birational aspects of the geometry of Mg (Gavril Farkas); The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces (Samuel Grushevsky and Igor Krichever); Brill-Noether theory (Joe Harris); GL+2(R)-orbit closures via topological splittings (Pascal Hubert, Erwan Lanneau, and Martin Moller); Harmonic mappings and moduli spaces of Riemann surfaces (Jurgen Jost and Shing Tung Yau); Algebraic structures on the topology of moduli spaces of curves and maps (Y.-P. Lee and R. Vakil); Recent development on the geometry of the Teichmuller and moduli spaces of Riemann surfaces (Kefeng Liu, Xiaofeng Sun, and Shing-Tung Yau); The universal properties of Teichmuller spaces (Vladimir Markovic and Dragomir Saric); Geometry of Teichmuller space with the Teichmuller metric (Howard Masur); GIT constructions of moduli spaces of stable curves and maps (Ian Morrison); Riemann surfaces, integrable hierarchies, and singularity theory (Yongbin Ruan). "Surveys in Differential Geometry: Volume 14, Geometry of Riemann surfaces and their moduli spaces" is an invaluable core addition to academic library Advanced Mathematics resource and reference collections and supplemental study lists in the specific field of Riemann Geometry.
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Computational conformal geometry is an emerging inter-disciplinary field, with applications to algebraic topology, differential geometry and Riemann surface theories applied to geometric modeling, computer graphics, computer vision, medical imaging, visualization, scientific computation, and many other engineering fields.

This new volume presents thorough introductions to the theoretical foundations -- as well as to the practical algorithms -- of computational conformal geometry. These have direct applications to engineering and digital geometric processing, including surface parameterization, surface matching, brain mapping, 3-D face recognition and identification, facial expression and animation, dynamic face tracking, mesh-spline conversion, and more. ... Read more

Customer Reviews (1)

Part of a simply outstanding series of eight such instructional texts
The need for 'student friendly' instructional texts in the field of mathematics is essential to the continued advancement of science in general, and the technologies upon which our 21st century are based. Now a joint publishing project of the International Press of Boston in cooperation with the Higher Education press of China, undergraduate and graduate level curriculums have access to a simply outstanding series of eight such instructional texts focused on updating the cutting edge of advances in mathematics entitled the 'Advanced Lectures in Mathematics' (ALM). The series consists of "Superstring Theory" comprised of lectures given by leading researchers (including Stephen Hawking and Edward Witten) on the subject; "Asymptotic Theory in Probability and Statistics with Applications" presenting eighteen papers organized into three major sections - limit theorems, statistics and applications, mathematical finance and insurance; "Computational Conformal Geometry" presenting succinct introductions to both its theoretical foundations and the practical applications; "Variational Principles for Discrete Surfaces" surveying among other thematically appropriate subjects, current research in the geometry of polyhedral surfaces with applications to computer graphics; "Fourth International Congress of Chinese Mathematicians" (publication pending); "Geometry, Analysis and Topology of Discrete Groups" featuring fifteen papers focusing on helping graduate students and researchers with the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces; "Handbook of Geometric Analysis No. 1" presenting papers on various aspects of geometric analysis; "Recent Developments in Algebra and Related Areas" comprised of fifteen papers delivered at the International conference on Algebra and Related Areas held at Tsinghua University, Beijing, China in August 2007. Although each volume is available individually, academic library reference collections should acquire the set in its entirety as seminal contributions to the field of higher mathematics for the benefit of the faculties and students they serve.
... Read more