Inspired by S S Chern : A Memorial Volume in Honor of a Great Mathematician.
Başlık:
Inspired by S S Chern : A Memorial Volume in Honor of a Great Mathematician.
Yazar:
Griffiths, Phillip A.
ISBN:
9789812772688
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (528 pages)
Seri:
Nankai Tracts in Mathematics ; v.11
Nankai Tracts in Mathematics
İçerik:
CONTENTS -- Preface -- Introduction -- Chapter 1: In Memory of Professor S. S. Chern -- Chapter 2: Twisted K-Theory and Cohomology -- 1. Introduction -- 2. The Action of the Automorphism Group -- 3. The Universal Fibration -- 4. The Atiyah-Hirzebruch Spectral Sequence -- 5. The Higher Differentials -- 6. Twisted Cohomology -- 7. The Chern Character -- 8. Chern Classes -- 9. Koschorke Classes -- 10. Operations in Twisted K-Theory -- 11. Appendix -- References -- Chapter 3: Yangian and Its Applications -- 1. Introduction -- 2. Yangian and RTT Relations -- 3. Applications of Yangian -- 4. Remarks -- Acknowledgement -- References -- Chapter 4: Geodesically Reversible Finsler 2-Spheres of Constant Curvature -- 1. Introduction -- 2. Structure Equations -- 3. A Double Fibration -- 4. Classification -- References -- Chapter 5: Multiple Solutions of the Prescribed Mean Curvature Equation -- Part 1 -- Part 2 -- References -- Chapter 6: On the Differentiability of Lipschitz Maps from Metric Measure Spaces to Banach Spaces -- 1. Introduction -- 2. Finite Dimensional Approximations and Weak Derivatives -- 3. Good Finite Dimensional Approximations -- 4. Differentiability for GFDA Targets -- 5. Bi-Lipschitz (Non)embedding for GFDA Targets -- 6. Appendix: Carnot Groups and Radon-Nikodym Targets -- References -- Chapter 7: Two-Forms on Four-Manifolds and Elliptic Equations -- 1. Background -- 2. A Class of Elliptic PDE -- 3. Examples -- 4. Partial Regularity Theory -- 5. Discussion -- References -- Chapter 8: Partial Connection for p-Torsion Line Bundles in Characteristic p > 0 -- 1. Introduction -- 2. A Partial Connection for p-Torsion Line Bundles -- References -- Chapter 9: Algebraic Cycles and Singularities of Normal Functions II -- I. Introduction.
II. The classical case of curves on a surface Part A -- III. The Classical Case Part B -- IV. Analysis of sing Vc on Fourfolds -- V. Maps in the Case of Fourfolds -- VI. Conclusions -- References -- Chapter 10: Planar Web Geometry Through Abelian Relations and Singularities -- 1. Introduction and Basic Objects -- 2. From Abelian Relations to Connections -- 3. Singularities of Webs Come on Stage -- References -- Chapter 11: Transitive Analytic Lie Pseudo-Groups -- 1. Introduction -- 2. Invariant Forms and the Cartan Structure Equations -- 3. An Infinite-Dimensional Lie Group Approach -- References -- Chapter 12: Stability of Closed Characteristics on Compact Convex Hypersurfaces -- 1. Introduction and Main Results -- 2. Equivariant Morse Theory for Closed Characteristics -- 3. Proof of the Main Theorem -- References -- Chapter 13: n-Invariant and Flat Vector Bundles II -- 1. Introduction -- 2. n-Invariant and the Variation Formula -- 3. n-Invariant and the Refined Analytic Torsion of Braverman-Kappeler -- References -- Chapter 14: On Planar Webs with Infinitesimal Automorphisms -- 1. Introduction and Statement of the Results -- 2. Generalities on Webs with Infinitesimal Automorphisms -- 3. Abelian Relations versus Infinitesimal Automorphisms -- 4. New Families of Exceptional Webs -- 5. Problems -- References -- Chapter 15: Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds Part II -- 1. Introduction -- 2. The Projective Alexander-Wermer Theorem -- 3. Theorems for General Projective Manifolds -- 4. Variants of the Main Hypothesis -- References -- Chapter 16: Aspects of Metric Geometry of Four Manifolds -- 1. Canonical Structure of 4-Manifolds -- 2. Topological Constraints -- 3. Curvature Estimates for Einstein Metrics.
4. Compactifying Moduli of Einstein 4-Manifolds -- 5. Complete Ricci-Flat 4-Manifolds -- 6. Problems on Ricci Flow in 4-Dimension -- 7. Anti-Self-Dual Metrics and Generalizations -- References -- Chapter 17: Algebrisation des tissus de codimension 1: la generalisation d'un theoreme de Bol -- 1. Introduction -- 2. La borne de Chern et une version precisee du Theoreme 1.1 -- 3. Rang maximal: conditions differentielles d'ordre un d'ordre deux -- 4. Debut de la demonstration: la methode standard -- 5. Suite de la demonstration: les courbes C(x) engendrent une surface -- 6. Fin de la demonstration -- References -- Chapter 18: Conformal Geometry and Fully Nonlinear Equations -- 1. The Yamabe Equation -- 2. A Fully Nonlinear Yamabe Problem -- 3. Variational Characterization -- 4. Liouville Theorems -- 5. Local Estimates -- 6. Dimension Four -- 7. Parabolic Methods -- 8. Positive Ricci Curvature -- 9. Admissible Metrics -- 10. The Negative Cone -- References -- Chapter 19: Memory of My First Research Teacher: The Great Geometer Chern Shiing-Shen -- Part I. Memory as a Student of Professor CHERN -- Part II. Generalized CHERN Classes and CHERN Numbers of Irreducible Complex Algebraic Varieties with Arbitrary Singularities -- References -- Chapter 20: Some Open Gromov-Witten Invariants of the Resolved Conifold -- 1. Introduction -- 2. Localizations on Moduli Spaces of Bordered Stable Maps to P1 -- 3. Reformulation of the Feynman Rule by the Marino-Vafa Formula -- 4. Free Field Realization of Feynman Rules -- 5. Other Operator Manipulations -- 6. Concluding Remarks -- References.
Özet:
Shiing-Shen Chern (1911-2004) was one of the leading differential geometers of the twentieth century. In 1946, he founded the Mathematical Institute of Academia Sinica in Shanghai, which was later moved to Nanking. In 1981, he founded the Mathematical Sciences Research Institute (MSRI) at Berkeley and acted as the director until 1984. In 1985, he founded the Nankai Institute of Mathematics in Tianjin. He was awarded the National Medal of Science in 1975; the Wolf Prize in mathematics in 1984; and the Shaw Prize in mathematical sciences in 2004. Chern's works span all the classic fields of differential geometry: the Chern-Simons theory; the Chern-Weil theory, linking curvature invariants to characteristic classes; Chern classes; and other areas such as projective differential geometry and webs that are mathematically rich but currently have a lower profile. He also published work in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds. Inspired by Chern and his work, former colleagues, students and friends - themselves highly regarded mathematicians in their own right - come together to honor and celebrate Chern's huge contributions. The volume, organized by Phillip Griffiths of the Institute for Advanced Study (Princeton), contains contributions by Michael Atiyah (University of Edinburgh), C-M Bai (Nankai), Robert Bryant (Duke University), Kung-Ching Chang (Peking University), Jeff Cheeger (New York University), Simon K Donaldson (Imperial College), Hélène Esnault (Universität Duisburg-Essen), Mo-Lin Ge (Nankai), Mark Green (University of California at Los Angeles), Phillip Griffiths (Institute for Advanced Study), F Reese Harvey (Rice University), Alain Hénaut (Université Bordeaux 1), Niky Kamran (McGill University), Bruce Kleiner (Yale), H Blaine Lawson, Jr (Suny at Stony Brook), Yiming Long (Nankai),
Xiaonan Ma (UMR 7640 du CNRS), Luc Pirio (IRMAR, France), Graeme Segal (Oxford), Gang Tian (MIT), Jean-Marie Trepreau (Institut de Mathématiques de Jussieu), Jeff Viaclovsky (MIT), Wei Wang (Nankai), Wentsun Wu (Chinese Academy of Sciences), C N Yang (Tsinghua), Tan Zhang (Murray State University), Weiping Zhang (Nankai) and others. Sample Chapter(s). Chapter 1: In Memory of Professor S. S. Chern (266 KB). Contents: In Memory of Professor S S Chern (C N Yang); Twisted K-Theory and Cohomology (M Atiyah); Yangian and Its Applications (C-M Bai et al.); Geodesically Reversible Finsler 2-Spheres of Constant Curvature (R L Bryant); Multiple Solutions of the Prescribed Mean Curvature Equation (K C Chang & T Zhang); On the Differentiability of Lipschitz Maps from Metric Measure Spaces to Banach Spaces (J Cheeger & B Kleiner); Two-Forms on Four-Manifolds and Elliptic Equations (S K Donaldson); Partial Connection for p -Torsion Line Bundles in Characteristic p > 0 (H Esnault); Algebraic Cycles and Singularities of Normal Functions, II (M Green & P Griffiths); Planar Web Geometry Through Abelian Relations and Singularities (A Hénaut); Transitive Analytic Lie Pseudo-Groups (N Kamran); Stability of Closed Characteristics on Compact Convex Hypersurfaces (Y Long & W Wang); η-Invariant and Flat Vector Bundles II (X Ma & W Zhang); On Planar Webs with Infinitesimal Automorphisms (D Marín et al.); Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part II (F R Harvey & H B Lawson, Jr); Aspects of Metric Geometry of Four Manifolds (G Tian); Algébrisation Des Tissus De Codimension 1: La Généralisation D'un Théorème De Bol (J-M Trépreau); Conformal Geometry and Fully Nonlinear Equations (J Viaclovsky); Memory of My First Research Teacher: The Great Geometer Chern Shiing-Shen (W Wu); Some Open Gromov-Witten Invariants of the
Resolved Conifold (J Zhou). Readership: Researchers in geometry.
Notlar:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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