Perspectives in mathematical sciences

273 Pages·2009·3.2 MB·English

by  N S Narasimha Sastry, et al

Perspectives in
Mathematical Sciences II
Pure Mathematics
Statistical Science and Interdisciplinary Research
Series Editor: Sankar K. Pal (Indian Statistical Institute)
Description:
In conjunction with the Platinum Jubilee celebrations of the Indian Statistical
Institute, a series of books will be produced to cover various topics, such as
Statistics and Mathematics, Computer Science, Machine Intelligence, Econometrics,
other Physical Sciences, and Social and Natural Sciences. This series of edited
volumes in the mentioned disciplines culminate mostly out of significant events —
conferences, workshops and lectures — held at the ten branches and centers of
ISI to commemorate the long history of the institute.
Vol. 1 Mathematical Programming and Game Theory for Decision Making
edited by S. K. Neogy, R. B. Bapat, A. K. Das & T. Parthasarathy
(Indian Statistical Institute, India)
Vol. 2 Advances in Intelligent Information Processing:
Tools and Applications
edited by B. Chandra & C. A. Murthy
(Indian Statistical Institute, India)
Vol. 3 Algorithms, Architectures and Information Systems Security
edited by Bhargab B. Bhattacharya, Susmita Sur-Kolay,
Subhas C. Nandy & Aditya Bagchi
(Indian Statistical Institute, India)
Vol. 4 Advances in Multivariate Statistical Methods
edited by A. SenGupta (Indian Statistical Institute, India)
Vol. 5 New and Enduring Themes in Development Economics
edited by B. Dutta, T. Ray & E. Somanathan
(Indian Statistical Institute, India)
Vol. 6 Modeling, Computation and Optimization
edited by S. K. Neogy, A. K. Das and R. B. Bapat
(Indian Statistical Institute, India)
Vol. 7 Perspectives in Mathematical Sciences I: Probability and Statistics
edited by N. S. N. Sastry, T. S. S. R. K. Rao, M. Delampady and
B. Rajeev (Indian Statistical Institute, India)
Vol. 8 Perspectives in Mathematical Sciences II: Pure Mathematics
edited by N. S. N. Sastry, T. S. S. R. K. Rao, M. Delampady and
B. Rajeev (Indian Statistical Institute, India)
Platinum Jubilee Series
Statistical Science and
Interdisciplinary Research - Vol. 8
Perspectives in
Mathematical Sciences II
Pure Mathematics
Editors
N. S. Narasimha Sastry
T. S. S. R. K. Rao
Mohan Delampady
B. Rajeev
Indian Statistical Institute, India
Series Editor: Sankar K. Pal
World Scientific
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Statistical Science and Interdisciplinary Research — Vol. 8
PERSPECTIVES IN MATHEMATICAL SCIENCES II
Pure Mathematics
Copyright © 2009 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ISBN-13 978-981-4273-64-0
ISBN-10 981-4273-64-3
Printed in Singapore.
Foreword
The Indian Statistical Institute (ISI) was established on 17th December,
1931byagreatvisionaryProfessorPrasantaChandraMahalanobistopro-
mote research in the theory and applications of statistics as a new scien-
tific discipline in India. In 1959, Pandit JawaharlalNehru, the then Prime
MinisterofIndiaintroducedtheISIActintheparliamentanddesignatedit
asanInstitution of National Importancebecauseofits remarkableachieve-
ments in statistical work as well as its contribution to economic planning.
Today, the Indian Statistical Institute occupies a prestigious position
in the academic firmament. It has been a haven for bright and talented
academicsworkingin anumber ofdisciplines. Its researchfaculty hasdone
IndiaproudinthearenasofStatistics,Mathematics,Economics,Computer
Science,amongothers.Overseventyfive years,ithas growninto amassive
banyan tree, like the institute emblem. The Institute now serves the na-
tion as a unified and monolithic organizationfromdifferent places,namely
Kolkata, the Headquarters, Delhi, Bangalore, and Chennai, three centers,
a network of five SQC-OR Units located at Mumbai, Pune, Baroda,
Hyderabad and Coimbatore, and a branch (field station) at Giridih.
The platinum jubilee celebrations of ISI have been launched by
Honorable Prime Minister Prof. Manmohan Singh on December 24, 2006,
andtheGovernmentofIndiahasdeclared29thJuneasthe“StatisticsDay”
to commemorate the birthday of Professor Mahalanobis nationally.
ProfessorMahalanobis,wasagreatbelieverininterdisciplinaryresearch,
because he thought that this will promote the development of not only
Statistics, but alsothe other naturalandsocialsciences.To promote inter-
disciplinary research, major strides were made in the areas of computer
science,statisticalqualitycontrol,economics,biologicalandsocialsciences,
physical and earth sciences.
The Institute’s motto of “unity in diversity”has been the guiding prin-
ciple of all its activities since its inception. It highlights the unifying role
of statistics in relation to various scientific activities.
v
vi Foreword
In tune with this hallowed tradition, a comprehensive academic pro-
gramme, involving Nobel Laureates, Fellows of the Royal Society, Abel
prize winner and other dignitaries, has been implemented throughout the
PlatinumJubilee year,highlightingthe emergingareasofongoingfrontline
research in its various scientific divisions, centers, and outlying units. It
includes international and national-level seminars, symposia, conferences
and workshops,as well as seriesof special lectures.As anoutcome of these
events, the Institute is bringing out a series of comprehensive volumes in
different subjects under the title Statistical Science and Interdisciplinary
Research, published by the World Scientific Press, Singapore.
The present volume titled Perspectives in Mathematical Sciences II:
Pure Mathematics is the eighth one in the series. The volume consists of
fifteen chapters, written by eminent mathematicians from different parts
of the world. These chapters cover a wide range of topics and provide a
current perspective of different areas of research, emphasizing the major
challenging issues. Some of the articles are written keeping the students
and the young researchers of mathematics in mind. I believe the state-of-
theartstudiespresentedinthisbookwillbeveryusefultobothresearchers
as well as practitioners.
Thanks to the contributors for their excellent research contributions,
andtothevolumeeditorsProfs.N.S.NarasimhaSastry,T.S.S.R.K.Rao,
M. Delampady and B. Rajeev for their sincere effort in bringing out the
volume nicely in time. Initial design of the cover by Mr. Indranil Dutta is
acknowledged.SincereeffortsbyProf.DilipSahaandDr.BarunMukhopad-
hyayforeditorialassistanceareappreciated.Thanks arealsodue to World
Scientific fortheir initiativeinpublishing the seriesandbeinga partofthe
Platinum Jubilee endeavor of the Institute.
December 2008 Sankar K. Pal
Kolkata Series Editor and
Director
Preface
Indian Statistical Institute, a premier research institute founded by Pro-
fessor Prasanta Chandra Mahalanobis in Calcutta in 1931, celebrated its
platinum jubilee during the year 2006-07. On this occasion, the institute
organized several conferences and symposia in various scientific disciplines
in which the institute has been active.
From the beginning, researchand training in probability, statistics and
related mathematical areas including mathematical computing have been
someofthemainactivitiesoftheinstitute.Overtheyears,thecontributions
fromthe scientistsofthe institute havehadamajorimpactonthese areas.
Asapartofthesecelebrations,theDivisionofTheoreticalStatisticsand
Mathematics of the institute decided to invite distinguished mathematical
scientists to contribute articles, giving “a perspective of their discipline,
emphasizingthe currentmajorissues”.Aconferenceentitled“Perspectives
in Mathematical Sciences” was also organized at the Bangalore Centre of
the institute during February 4-8, 2008.
The articles submitted by the speakers at the conference, along with
the invited articles, are brought together here in two volumes (Part I and
Part II).
PartIconsistsofarticlesinProbabilityandStatistics.ArticlesinStatis-
tics are mainly on statistical inference, both frequentist and Bayesian, for
problems of current interest. These articles also contain applications illus-
trating the methodologies discussed. The articles on probability are based
ondifferent“probabilitymodels”arisinginvariouscontexts(machinelearn-
ing, quantum probability, probability measures on Lie groups, economic
phenomena modelled on iterated random systems, “measure free martin-
gales”, and interacting particle systems) and represent active areas of re-
search in probability and related fields.
Part II consists of articles in Algebraic Geometry, Algebraic Number
Theory, Functional Analysis and Operator Theory, Scattering Theory,
vii
viii Preface
von Neumann Algebras, Discrete Mathematics, Permutation Groups, Lie
Theory and Super Symmetry.
All the authors have taken care to make their exposition fairly self-
contained. It is our hope that these articles will be valuable to researchers
at various levels.
The editorial committee thanks all the authors for writing the articles
andsendingthemintime,thespeakersattheconferencefortheirtalksand
various scientists who have kindly refereed these articles. Thanks are also
due to the National Board for Higher Mathematics, India, for providing
partial support to the conference.Finally, we thank Ms. Asha Lata for her
help in compiling these volumes.
October 16, 2008 N. S. Narasimha Sastry
T. S. S. R. K. Rao
Mohan Delampady
B. Rajeev
Contents
Foreword v
Preface vii
1. Use of Resultants and Approximate Roots for Doing the
Jacobian Problem 1
S. S. Abhyankar
2. Monodromy of Principal Bundles 17
I. Biswas and A. J. Parameswaran
3. Oligomorphic Permutation Groups 37
P. J. Cameron
4. Descriptive Set Theory and the Geometry of Banach Spaces 63
G. Godefroy
5. Multiplicity-Free Homogeneous Operators in the Cowen-
Douglas Class 83
A. Kor´anyi and G. Misra
6. The Standard Conjectures on Algebraic Cycles 103
M. S. Narasimhan
ix