Perspectives in Mathematical Science Ii : Pure Mathematics.
Başlık:
Perspectives in Mathematical Science Ii : Pure Mathematics.
Yazar:
Sastry, N. S. Narasimha.
ISBN:
9789814273657
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (281 pages)
Seri:
Statistical Science and Interdisciplinary Research ; v.8
Statistical Science and Interdisciplinary Research
İçerik:
Contents -- Foreword -- Preface -- 1. Use of Resultants and Approximate Roots for Doing the Jacobian Problem S. S. Abhyankar -- 1.1. Introduction -- 1.2. Basic Technique -- 1.3. Resultants and Discriminants -- 1.4. Real Numbers and Approximate Roots -- Epilogue -- References -- 2. Monodromy of Principal Bundles I. Biswas and A. J. Parameswaran -- 2.1. Introduction -- 2.2. Tannakian Category -- 2.3. A Tannakian Category for a Pointed Curve -- 2.4. Monodromy of a Strongly Semistable Principal Bundles -- 2.5. More on Monodromy -- 2.6. Bundles on Higher Dimensional Varieties -- References -- 3. Oligomorphic Permutation Groups P. J. Cameron -- 3.1. Introduction -- 3.1.1. Permutation groups -- 3.1.2. Oligomorphic permutation groups -- 3.1.3. Topology -- 3.1.4. Cycle index -- 3.2. Connections -- 3.2.1. Model theory -- 3.2.2. Combinatorial enumeration -- 3.3. Constructions -- 3.3.1. Direct and wreath products -- 3.3.2. Other examples -- 3.4. Growth Rates -- 3.5. Graded Algebras -- 3.6. Group Structure -- References -- 4. Descriptive Set Theory and the Geometry of Banach Spaces G. Godefroy -- 4.1. Introduction -- 4.2. A Short Survey on Analytic Sets -- 4.3. Bossard's Coding of Separable Banach Spaces -- 4.4. Coanalytic Ranks -- 4.5. A New Direction: The Converse Statements -- Acknowledgment -- References -- 5. Multiplicity-Free Homogeneous Operators in the Cowen- Douglas Class A. Korányi and G. Misra -- 5.1. Background Material -- 5.2. Computation of the Multipliers for the Unit Disc -- 5.3. Conditions Imposed by the Reproducing Kernel -- 5.4. The Multiplicity-Free Case -- 5.5. Examples -- References -- 6. The Standard Conjectures on Algebraic Cycles M. S. Narasimhan -- 6.1. The Case of Complex Projective Varieties -- 6.2. Standard Conjectures in Abstract Algebraic Geometry -- References.
7. On the Classification of Binary Shifts on the Hyperfinite II 1 Factor G. L. Price -- 7.1. Introduction -- 7.2. Preliminaries -- 7.3. Bitstreams and Polynomials -- 7.4. Counting Polynomials with Symmetry -- 7.5. Conjugacy Classes of Binary Shifts -- References -- 8. Symmetric and Quasi-Symmetric Designs and Strongly Regular Graphs S. S. Sane -- 8.1. Introduction and Preliminaries -- 8.2. Symmetric Designs -- 8.3. Strongly Regular Graphs -- 8.4. Quasi-Symmetric Designs -- Acknowledgments -- References -- 9. Perturbation Determinant, Krein's Shift Function and Index Theorem K. B. Sinha -- 9.1. Introduction -- 9.2. Perturbation Determinant -- 9.3. Witten Index and Its Invariance -- 9.4. Krein's Shift Function -- 9.5. Application to Quantum Mechanics and Generalized Levinson's Theorem -- References -- 10. Zero Cycles and Complete Intersection Points on A.ne Varieties V. Srinivas -- References -- 11. Root Numbers and Rational Points on Elliptic Curves R. Sujatha -- 11.1. Elliptic Curves and the Birch and Swinnerton-Dyer Conjecture -- 11.2. Congruent Number Problem -- 11.3. Root Numbers and the Parity Conjecture -- 11.4. Recent Results -- 11.5. Examples and Applications -- References -- 12. von Neumann Algebras and Ergodic Theory V. S. Sunder -- References -- 13. Gutzmer's Formula and the Segal-Bargmann Transform S. Thangavelu -- 13.1. Introduction -- 13.2. Segal-Bargmann Transform on the Heisenberg Group -- 13.3. Gutzmer Formulas and Their Applications -- References -- 14. Finite Translation Generalized Quadrangles J. A. Thas -- 14.1. Finite Generalized Quadrangles -- 14.1.1. Finite generalized quadrangles -- 14.1.2. Grids and dual grids -- 14.1.3. The classical generalized quadrangles -- 14.1.4. Ovals, hyperovals and ovoids -- 14.1.5. The generalized quadrangles T2(O) and T3(O) of Tits -- 14.1.6. The generalized quadrangles T. 2 (O).
14.1.7. Orders of the known generalized quadrangles -- 14.1.8. Generalized quadrangles with small parameters -- 14.2. Translation Generalized Quadrangles -- 14.2.1. Translation generalized quadrangles -- 14.2.2. The kernel of a translation generalized quadrangle -- 14.2.3. T(n,m, q)s and translation generalized quadrangles -- 14.2.4. Regular pseudo-ovals and regular pseudo-ovoids -- 14.3. Important Properties of O(n,m, q) -- 14.3.1. Properties of O(n,m, q) -- 14.3.2. Properties of pseudo-ovals -- 14.3.3. Properties of eggs -- 14.4. Eggs O(n, 2n, q): Fundamental Results and Characterizations -- 14.4.1. Characterizations of regular eggs O(n, 2n, q) -- 14.4.2. Fundamental results on eggs -- 14.5. Pseudo-Ovals: Old and New Results -- 14.5.1. Old results -- 14.5.2. New results -- References -- 15. Super Geometry as the Basis for Super Symmetry V. S. Varadarajan -- 15.1. Introduction -- 15.2. Super Geometry -- 15.3. Super Symmetric Extensions of Relativistic Theories and Super Poincaré Groups -- 15.4. Classification of Super Particles -- 15.5. UIR's of Regular Super Semi Direct Products -- References -- Author Index -- Subject Index -- Contents of Part I.
Özet:
This book presents a collection of invited articles by distinguished Mathematicians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute, during the year 2007. These articles provide a current perspective of different areas of research, emphasizing the major challenging issues. Given the very significant record of the Institute in research in the areas of Statistics, Probability and Mathematics, distinguished authors have very admirably responded to the invitation. Some of the articles are written keeping students and potential new entrants to an area of mathematics in mind. This volume is thus very unique and gives a perspective of several important aspects of mathematics. Sample Chapter(s). Foreword (78 KB). Chapter 1: Use of Resultants and Approximate Roots for Doing the Jacobian Problem (262 KB). Contents: Use of Resultants and Approximate Roots for Doing the Jacobian Problem (S S Abhyankar); Monodromy of Principal Bundles (I Biswas & A J Parameswaran); Oligomorphic Permutation Groups (P J Cameron); Descriptive Set Theory and the Geometry of Banach Spaces (G Godefroy); Multiplicity-Free Homogeneous Operators in the Cowen-Douglas Class (A Korányi & G Misra); The Standard Conjectures on Algebraic Cycles (M S Narasimhan); On the Classification of Binary Shifts on the Hyperfinite II 1 Factor (G L Price); Symmetric and Quasi-Symmetric Designs and Strongly Regular Graphs (S S Sane); Perturbation Determinant, Krein's Shift Function and Index Theorem (K B Sinha); Zero Cycles and Complete Intersection Points on Affine Varieties (V Srinivas); Root Numbers and Rational Points on Elliptic Curves (R Sujatha); von Neumann Algebras and Ergodic Theory (V S Sunder); Gutzmer's Formula and the Segal-Bargmann Transform (S Thangavelu); Finite Translation Generalized Quadrangles (J A Thas); Super Geometry as the Basis for Super
Symmetry (V S Varadarajan). Readership: Graduate students and researchers with an interest in pure mathematics.
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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