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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles!Shing-Tung Yau ( born April 4, 1949) is a Chinese American mathematician working in differential geometry. He was born in Shantou, Guangdong Province, China into a family of scholars from Jiaoling, Guangdong Province. Yau has impacts on both physics and mathematics. Calabi-Yau manifolds are among the 'standard toolkit' for string theorists today. He has been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated-sixty years after its discovery-that Einstein's theory is consistent and stable. His proof of the Calabi conjecture allowed physicists-using Calabi-Yau compactification-to show that string theory is a viable candidate for a unified theory of nature. ... Read more

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ContentsAnomalous diffusion and stability of Harnack inequalities(by M.T. Barlow)From isoperimetric inequalities to heat kernels via symmetrization(by G. Besson)Discrete isoperimetric inequalities(by F. Chung)An excursion into geometric analysis(by T.H. Colding & W.P. Minicozzi II)Eigenvalues of elliptic operators and geometric applications(by A. Grigor'yan, Y. Netrusov & S.-T. Yau)Spectral gap, logarithmic Sobolev constant, and geometric bounds(by M. Ledoux)Discrete analytic functions: An exposition(by L. Lovász)Conformal properties in classical minimal surface theory(by W.H. Meeks III & J. Pérez)Analysis of the cut locus via heat kernel(by R. Neel & D. Strook)Analysis on Riemannian co-compact covers(by L. Saloff-Coste)Functoriality and small eigenvalues of Laplacian on Riemann surfaces(by F. Shahidi)The inverse spectral problem(by S. Zelditch) ... 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.

As a service to the mathematics community, the editors of the Journal of Differential Geometry decided to organize a conference to be held every three years. Among the speakers at our first conference were people working in algebraic geometry, mathematical physics and other interesting fields. These speakers are prominent specialists in their respective areas who are able to give a broad overview of recent trends and make predictions and suggestions for future research. We believe that these conferences are important gatherings that inspire experts and non-experts alike. Our first conference was held at Harvard University from April 27-29, 1990, was made possible by the generous funding of the Journal of Differential Geometry. Central to the success of this conference were the speakers who prepared not only two hours' worth of lectures, but also the manuscripts published here. Their lectures were enthusiastically received by several hundred participants. ... Read more

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These three parts contain the proceedings of the AMS Summer Institute on Differential Geometry, held at the University California, Los Angeles in July 1990. This was the largest AMS Summer Institute ever, reflecting the wide-ranging and intense research activity in the subject. The parts contain many extensive survey articles presenting perspectives on relatively broad topics; these articles would be accessible to advanced graduate students. In addition, the authors of the research articles were encouraged to survey the relevant literature. The three parts together offer the deepest and most comprehensive survey of recent research in differential geometry available today. ... Read more

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ContentsOn the conformal scalar curvature equation and related problems(by S. Brendle)A survey of the Kähler-Ricci Flow and Yau's Uniformization Conjecture(by A. Chau, L.-F. Tam)Recent developments on the Hamilton's Ricci Flow(by H.-D. Cao, B.-L. Chen, and X.-P. Zhu)Curvature flows in semi-Riemannian manifolds(by C. Gerhardt)Global regularity and singularity development for wave maps(by J. Krieger)Relativistic Teichmüller theory: a Hamilton-Jacobi approach to 2+1-dimensional Einstein gravity(by V. Moncrief)Monotonicity and Li-Yau-Hamilton inequalities(by L. Ni)Singularities of mean curvature flow and flow with surgeries(by C. Sinestrari)Some recent developments in Lagrangian mean curvature flows(by M.-T. Wang) ... Read more

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ContentsThe geometry of classical particles(by M. Atiyah)Singularities in the work of Friedrich Hirzebruch(by E. Brieskorn)The moduli space of abelian varieties and the singularities of the theta divisor(by C. Gilberto & G. Van der Geer)Holomorphic spheres in loop groups and Bott periodicity(by R.L. Cohen, E. Lupercio & G.B. Segal)Moment map and diffeomorphisms(by S.K. Donaldson)Dirac charge quantization and generalized differential cohomology(by D.S. Freed)The holomorphic kernel of the Rankin-Selberg convolution(by D. Goldfeld & S. Zhang)Equivariant de Rham theory and graphs(by V. Guillemin & C. Zara)Morse theory and Stokes' theorem(by F.R. Harvey & H.B. Lawson, Jr)The Atiyah-Bott-Singer fixed point theorem and number theory(by F. Hirzebruch)The moduli space of complex Lagrangian submanifolds(by N.J. Hitchin)Which Singer is that?(by R.V. Kadison)Curvature and function theory on Riemannian manifolds(by P. Li)Mirror Principle. III(by B.H. Lian, K. Liu & S.-T. Yau)Mirror Principle. IV(by B.H. Lian, K. Liu & S.-T. Yau)Three constructions of Frobenius manifolds: A comparative study(by Yu.I. Manin)On Ricci-flat twistor theory(by R. Penrose)On the geometry of nilpotent orbits(by W. Schmid & K. Vilonen)Seiberg-Witten invariants, self-dual harmonic 2-forms and Hofer-Wysocki-Zehnder formalism(by C.H. Taubes)Unifying themes in topological field theories(by C. Vafa)Noncommutative Yang-Mills theory and string theory(by E. Witten) ... Read more

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ContentsProjective planes, Severi varieties and spheres(by M. Atiyah & J. Berndt)Degeneration of Einstein metrics and metrics with special holonomy(by J. Cheeger)The min-max construction of minimal surfaces(by T.H. Colding & C. De Lellis)Universal volume bounds in Riemannian manifolds(by C.B. Croke & M. Katz)A Kawamata-Viehweg vanishing theorem on compact Kähler manifolds(by J.-P. Demailly & T. Peternel)Moment maps in differential geometry(by S.K. Donaldson)Local rigidity for cocycles(by D. Fisher & G.A. Margulis)Einstein metrics, four-manifolds, and differential topology(by C. LeBrun)Topological quantum field theory for Calabi-Yau threefolds and G2-manifold(by N.C. Leung)Geometric results in classical minimal surface theory(by W.H. Meeks III)On global existence of wave maps with critical regularity(by A. Nahmod)Discreteness of minimal models of Kodaira dimension zero and subvarieties of moduli stacks(by E. Viehweg & K. Zuo)Geometry of the Weil-Peterson completion of Teichmüller space(by S.A. Wolpert) ... Read more

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Chapters: Zhu Shijie, Zhang Heng, Zu Chongzhi, Shen Kuo, Shing-Tung Yau, Guo Shoujing, Xu Guangqi, Yi Xing, Shiing-Shen Chern, Liu Hui, Li Zhi, Chia-Chiao Lin, Yang Hui, Li Chunfeng, Jing Fang, Pao Ming Pu, Feng Kang, Ky Fan, Hao Wang, Chen Jiangong, Wu Wenjun, M. T. Cheng, Chen Jingrun, Gang Tian, Yum-Tong Siu, Shige Peng, Wang Yuan, Hua Luogeng, Fan Chung, Hu Hesheng, Qin Jiushao, Zhan Tao, Shi Zhongci, Wang Xiaotong, Sun Zhiwei, Zhu Xiping, C. C. Li, Jian-Shu Li, Wei-Liang Chow, Huang Daren, Jia Rongqing, Su Buqing, Jia Xian, Xiong Qinglai, Daqing Wan, Li Shanlan, Zu Gengzhi, Jie-Zhong Zou, Zeng Jiongzhi, Gu Chaohao, Wang Fan, Ke Zhao, Sun Tzu, Sun Zhihong, Sun Guangyuan, Jinchao Xu. Source: Wikipedia. Pages: 238. 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: Shen Kuo or Shen Gua (Chinese: ; pinyin: Shn Kuò; Wade-Giles: Shen K'uo) (10311095), style name Cunzhong () and pseudonym Mengqi (now usually given as Mengxi) Weng (), was a polymathic Chinese scientist and statesman of the Song Dynasty (9601279). Excelling in many fields of study and statecraft, he was a mathematician, astronomer, meteorologist, geologist, zoologist, botanist, pharmacologist, agronomist, archaeologist, ethnographer, cartographer, encyclopedist, general, diplomat, hydraulic engineer, inventor, academy chancellor, finance minister, governmental state inspector, poet, and musician. He was the head official for the Bureau of Astronomy in the Song court, as well as an Assistant Minister of Imperial Hospitality. At court his political allegiance was to the Reformist faction known as the New Policies Group, headed by Chancellor Wang Anshi (10211086). In his Dream Pool Essays (; Mengxi Bitan) of 1088, Shen was the first to describe the magnetic needle compass, which would be used for navigation (first described in Euro...More: http://booksllc.net/?id=1102000 ... Read more

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Chapters: Chen Duxiu, Shing-Tung Yau, Wang Ganchang, Tsung-Dao Lee, Chien-Shiung Wu, List of Presidents of Zhejiang University, Shiing-Shen Chern, Shu Xingbei, Ma Yinchu, Lu Yongxiang, Huang Minlon, Zing-Yang Kuo, Han Qing-Quan, Chen Jiangong, Tan Jiazhen, Wu Wenjun, Li Hsi-Mou, M. T. Cheng, Jin Au Kong, Zheng Xiaocang, Shao Peizi, Wang Guosong, Chen Daqi, Li Shouheng, Sha Wenhan, Hu Haichang, Edgar Tang, Ho Ping-Sung, Lin Fanghua, Lu Guanqiu, Hu Jimin, Wu Dingliang, Chen Ziyuan, Kefeng Liu, Ren Mei'e, Lo Tsung-Lo, Tien-Fong Cheng, Han Zhenxiang, Binghui Shen, Xu-Jia Wang, Li Enliang, Shi Zhongci, Coching Chu, Bei Shizhang, List of Zhejiang University Faculty, Liu Chen, Hu Zhuangyou, Yang Wei, Ba Denian, Jian-Shu Li, Huang Daren, Jiang Menglin, He Weifang, Chen Hang, Zhou Rongxin, Xia Yan, Pan Yunhe, Sha Menghai, Liu Yizheng. Source: Wikipedia. Pages: 202. 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: Shing-Tung Yau (Chinese: ; born April 4, 1949) is a Chinese American mathematician working in differential geometry. He was born in Shantou, Guangdong Province, China into a family of scholars from Jiaoling, Guangdong Province. Yau has made lasting impacts on both physics and mathematics. Calabi-Yau manifolds are among the standard toolkit for string theorists today. He has been very active in the exciting interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity finally demonstratedsixty years after its discoverythat Einsteins theory is consistent and stable. His proof of the Calabi conjecture allowed physicistsusing Calabi-Yau compactificationto show that string theory is a viable candidate for a unified theory of nature. Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family ...More: http://booksllc.net/?id=303137 ... Read more

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Kapitel: Chen Ning Yang, John Willard Milnor, Michail Leonidowitsch Gromow, Shing-Tung Yau, Axel Meyer, Dennis Sullivan, Melba Phillips, Detlef Gromoll, Michael Kimmel, Oleg Janowitsch Wiro, Rose Laub Coser, Massimo Pigliucci, Paul Christian Lauterbur, Jeff Cheeger, Anthony Knapp, Robert Schatten, Barry Mccoy, Bernard Maskit, Mark Aronoff, Douglas J. Futuyma. Aus Wikipedia. Nicht dargestellt. Auszug: Chen-Ning Franklin Yang (simplified Chinese: ; traditional Chinese: ; pinyin: Yáng Zhènníng) (born October 1, 1922) is a Chinese-American physicist who worked on statistical mechanics and particle physics. He, together with Tsung-dao Lee, received the 1957 Nobel prize in physics for their work on parity nonconservation of weak interaction. Yang naturalized as a United States citizen in 1964. Yang was born in Hefei, Anhui, China, his father Yang Ko-Chuen (simplified Chinese: ; pinyin: Yáng Wǔzhī) (1896-1973) was a mathematician and his mother Luó Mènghuà (罗孟华) was a housewife. Yang attended elementary school and high school in Beijing, and in the autumn of 1937 his family moved to Hefei after Japanese invaded China. In 1938 they moved to Kunming, Yunnan, where the National Southwestern Associated University was located. In the same year, as a second year student, Yang passed the entrance examination and studied at the National Southwestern Associated University. He received his bachelor's degree in 1942, the thesis being about the application of group theory to molecular spectra, under the supervision of Wu Ta-you (吴大猷) (1907-2000). He continued to study graduate courses there for two years under the supervision of Wang Zhuxi (王竹溪) (1911-1983), working on statistical mechanics. In 1944 he received his master's degree was awarded a scholarship known as the Boxer Indemnity (simplified Chinese: ; traditional Chinese: ; pinyin: Gēngzǐ péikuǎn), a scholarship set up by the United States government using the funds raised from the money C...http://booksllc.net/?l=de ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Shen Kuo, Su Song, Shiing-Shen Chern, Chen Jingrun, Zhang Heng, Zu Chongzhi, Sun Zi, Shing-Tung Yau, Zhu Shijie, Liu Hui, Qin Jiushao, Yang Hui. Non illustré. Mises à jour gratuites en ligne. Extrait : Shen Kuo (chinois : , pinyin : ), Shen K'uo, Shen Kua ou encore Shen Gua (Hangzhou, 1031 - Zhenjiang, 1095) est un scientifique polymathe chinois et un fonctionnaire gouvernemental sous la dynastie Song (960-1279). Homme d'esprit universel, il fut notamment géologue, astronome, mathématicien, cartographe, inventeur, météorologue, agronome, ethnographe, zoologiste, botaniste, ingénieur en hydraulique, pharmacologue, auteur encyclopédiste, poète, musicien, diplomate, général, chancelier académique, ministre des finances et inspecteur des services de l'État. Il fut également responsable du Bureau de l'Astronomie à la cour des Song, ainsi qu'adjoint du ministre de l'Hospitalité impériale. À la cour, son allégeance politique allait à la faction réformiste du « Groupe de nouvelles politiques », dirigée par le chancelier Wang Anshi ( ; 1021-1086). Dans son livre Mengxi Bitan () de 1088, Shen est le premier à décrire le compas à aiguille magnétique qui sera utilisé pour la navigation alors qu'en Europe, cette découverte ne sera décrite pour la première fois qu'en 1187 par Alexandre Neckam. Shen a aussi découvert le concept du « vrai Nord » en termes de déclinaison magnétique vers le pôle Nord, c'est-à-dire en découvrant qu'il existe une différence entre le pôle Nord géographique et le pôle Nord magnétique. Ce fut un pas décisif dans l'Histoire pour faire du compas un outil de navigation encore plus utile, alors que cette notion resta encore inconnue en Europe les quatre siècles suivants (Christophe Colomb). Parallèlement à son ...http://booksllc.net/?l=fr ... Read more

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Chapters: Rosanna Wong, Shing-Tung Yau, Wong Jing, Ricky Wong Wai Kay, Tsui Lap-Chee, Chung King Fai, Gary Chan, Yu Ying-Shih, Priscilla Leung, Norman Chan, Lee Ming-Kwai, John Tong Hon, Cheun-Yan Cheng, Vincent Cheng, Joseph Sung, Edward Tsang, Leung Ka-Lau, Chan Yuk-Shee, Rebecca Chiu, Kitty Poon, Samson Tam, Tso Wung-Wai, Paul Chan, Bruce Liu, Yeung Yiu-Chung, Florence Hui, Sin Chung Kai, Cho Chun-Ying, Lavender Cheung, Kwong Chi Kin, Heidi Chu, Louisa Wong, Ruby Wu, Cheung Pui Ling. Source: Wikipedia. Pages: 125. 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: Dame Rosanna Wong Yick-ming, DBE, JP (born 15 August 1952), also known by her married name Mrs Rosanna Tam Wong Yick-ming in her former marriage from 1979 lasting until 1992, and primarily known as Dr Rosanna Wong in public occasions after 1997, is a Hong Kong social work administrator and politician who has served as the Executive Director of the Hong Kong Federation of Youth Groups since 1980. Before the transfer of sovereignty of Hong Kong, she was appointed as unofficial member of the Legislative Council from 1985 to 1991 and of the Executive Council from 1988 to 1991. She briefly retired from politics in 1991 but was successful to return as unofficial Executive Councillor for a second time in 1992, and was also appointed chairperson of the Hong Kong Housing Authority in the following year. Wong was trusted by the last British colonial Governor of Hong Kong, Chris Patten (later Lord), who chose her to replace Baroness Dunn as the Convenor of the Executive Council (equivalent to the Senior Unofficial Member of the Executive Council) in 1995, thus rising as an influential figure in the final years of the colonial government. In 1997, she was made Dame Commander of the Order of the British Empire and became the second Chinese ...More: http://booksllc.net/?id=20343233 ... Read more

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Chapters: Shing-Tung Yau, Shiu-Yuen Cheng, Juncheng Wei. Source: Wikipedia. Pages: 23. 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: Shing-Tung Yau (Chinese: ; born April 4, 1949) is a Chinese American mathematician working in differential geometry. He was born in Shantou, Guangdong Province, China into a family of scholars from Jiaoling, Guangdong Province. Yau has made lasting impacts on both physics and mathematics. Calabi-Yau manifolds are among the standard toolkit for string theorists today. He has been very active in the exciting interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity finally demonstratedsixty years after its discoverythat Einsteins theory is consistent and stable. His proof of the Calabi conjecture allowed physicistsusing Calabi-Yau compactificationto show that string theory is a viable candidate for a unified theory of nature. Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family of eight children. When he was only a few months old, his family emigrated to Hongkong, where they lived first in Yuen Long and then 5 years later in Shatin. When Yau was fourteen, his father, a philosophy professor, died. After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969. Yau went to UC Berkeley in the fall of 1969. At the age of 22, Yau was awarded the Ph.D. degree under the supervision of Shiing-Shen Chern at Berkeley in two years. He spent a year as a member of the Institute for Advanced Study, Princeton, New Jersey, and two years at the State University of New York at Stony Brook. Then he went to Stanford University. Since 1987, he has been at Harvard University, where he has had numerous Ph...More: http://booksllc.net/?id=303137 ... Read more

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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.2010 paperback re-issue. ... Read more

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The conference, held at the Chinese University of Hong Kong, on which these proceedings are based was organized in response to Andrew Wiles' conjecture that every elliptic curve over Q is modular. The final difficulties in the proof of the conjectural upper bound for the order of the Selmer group attached to the symmetric square of a modular form, have since been overcome by Wiles with the assistance of R. Taylor. The proof that every semi-stable elliptic curve over Q is modular is not only significant in the study of elliptic curves, but also due to the earlier work of Frey, Ribet, and others, completes a proof of Fermat's last theorem.New paperback re-issue of the revised second edition.CONTENTSForeword by John Coates and Shing-Tung YauFermat's Last Theorem(by H. Darmon, F. Diamond, R. Taylor)Characteristic distributions for non-torsion Lamda-modules(by P. Balister)On the symmetric square of a modular elliptic curve(by J. Coates, A. Sydenham)The refined conjecture of Serre(by Fred Diamond)Wiles minus epsilon implies Fermat(by Norm Elkies)Geometric Galois representations(by J.M. Fontaine, B. Mazur)On elliptic curves(by Gerhard Frey )Complete intersections and Gorenstein rings(by H.W. Lenstra, Jr.)Homologic des courbes modulaires(by L. Merel)Irreducible Galois representation(by Kenneth A. Ribet)Mod p representations of elliptic curves(by K. Rubin, A. Silverberg)A review of non-Archimedean elliptic functions(by John Tate)On Galois representations associated to Hilbert modular forms II(by Richard Taylor) ... Read more