Perspectives in mathematical sciences . II / / editors, N.S. Narasimha Sastry ... [et al.] ; series editor: Sankar K. Pal

• Record Nr.: UNINA9910811308203321
• Pubbl/distr/stampa: Singapore ; ; London, : World Scientific, c2009
• ISBN: 1-282-75810-1; 9786612758102; 981-4273-65-1
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (281 p.)
• Collana: Statistical science and interdisciplinary research ; ; v. 8
• Altri autori (Persone): Narasimha SastryN. S
• Disciplina: 510; 519.2
• Soggetti: Probabilities; Statistics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Platinum jubilee series".
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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. Cameron3.1. 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 StatementsAcknowledgment; ; 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. Price7.1. 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 Determinant9.3. 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
• Sommario/riassunto: 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 ma