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RAMANUJAN INSTITUTE FOR ADVANCED STUDY IN MATHEMATICS http://www.unom.ac.in

A humble beginning of the Ramanujan Institute of Mathematics (as one of the educational institutions governed by the Asoka Charitable Trust, Karaikudi) at "Krishna Vilas", Vepery, Madras was made by Dr. Rm. Alagappa Chettiar on 26 January 1950 as a memorial to the mathematical genius Srinivasa Ramanujan. A formal Inauguration of the Ramanujan Institute of Mathematics was held on 15 April 1950 by Dr.A.Lakshmanaswamy Mudaliar, Vice Chancellor of University of Madras and Dr. T.Vijayaraghavan, student of G.H.Hardy, was appointed as Director of the Institute. It was located at "Krishna Vilas", Vepery. The Institute started on a modest scale with one professor, one lecturer and two research scholars on the staff. In a short span of five to six years the Institute became well known for its significant work in mathematical analysis. On 1 January 1951, a noted analyst Professor C.T. Rajagopal was invited to join the Institute.

The Nobel laureate Prof. S.Chandrasekar was always a sincere well wisher of the Institute and was keenly interested in its development. The Institute started making its presence felt and prominent among the visitors to the Department during this period was the noted number theorist Dr. S.S.Pillai who delivered lectures on 25, 26 and 27 July, 1950 between 5.30.P.M. and 6.30 P.M. on Convergence (almost everywhere) of a Fourier Series and Allied Problems. Professor V.Ganapathy Iyer, another analyst, delivered lectures on 3 Oct 1951 at 4.30 p.m. on the topic Generalities, Topologies and Linear spaces, 4 & 5 Oct 1951 at 8.00 a.m. on Linear Space of Integral Functions and 6 Oct 1951 at 8.00 a.m. on Banach Algebras of Summation Process. Another notable visitor to the Institute was Dr. Norbert Wiener who visited the Institute in 1953. Infact on 5th Feb. 1953 he wrote a letter to Dr.S.S.Bhatnagar regarding the maintenance of the Institute.

On 1 April 1953 Dr. T.Vijayaraghavan occupied the Chair created by the Ministry of Education. When he passed away on 20 April 1955, the grant for Chair was stopped as there was no matching grant from the Institute run by the Asoka Charitable Trust. Subsequently on 21 April 1955 Professor C.T.Rajagopal was appointed as Director of the Institute on the recommendations of Professors Andre Weil, Princeton and S.Chandrasekhar, Noble Laureate.

Unfortunately, in a letter dated 10 November 1956 Asoka Charitable Trust expressed its inability to run Ramanujan Institute even though Dr.Rm. Alagappa Chettiar had agreed to maintain the Institute upto April 1957. But Dr. Rm. Alagappa Chettiar passed away in the first week of April 1957 and the Institute faced a financial crisis. Prof. C.T.Rajagopal continued his efforts untiringly to secure funds for the Institute. Dr.S. Chandrasekhar gave his strong support to secure financial assistance and funds were supplied by the Ministry of Education, Government of India. Thanks to the initiative taken by Pandit Jawaharlal Nehru who persuaded the then Vice-Chancellor Dr.A. Lakshmanaswamy Mudaliar, the management of the Institute came to be vested with the University of Madras. On 1 May 1957 the Institute was taken over by the University of Madras, thanks to the efforts by Dr.S.Chandrasekhar and Pandit Jawaharlal Nehru. Department of Mathematics and Ramanujan Institute of Mathematics (1957-1966) During the period 1957-66, the Department of Mathematics and the Ramanujan Institute of Mathematics were functioning as two independent bodies under the University of Madras. Dr. V.K.Balachandran succeeded Dr.V.S.Krishnan as Head of the Department of Mathematics in 1964 while Prof. C.T.Rajagopal continued to be the Director of the Ramanujan Institute till 1966.

In a letter dated 1 November 1958 Ramanujan Professorship to Ramanujan Institute of Mathematics was created by the Ministry of Scientific Research and Cultural Affairs but could not be filled up. The Institute had close contact with almost all Universities and premier Research Institutions in India. The Institute had also developed contacts with some of the international centers for mathematical learning. Ramanujan Institute for Advanced Study in Mathematics (1967-2005) The activities of the Ramanujan Institute for Advanced Study in Mathematics as a UGC-SAP (CAS Center) have been traced from the year 1967 in six periods.

1967 - 1977, 1978 - 1984, 1985 - 1989, 1992 - 1997 ( I Phase), 1998 - 2003 (II Phase), 2004 - 2009 (III Phase),

1967-1977

In 1967 the University Grants Commission of India came up with the concrete proposal of making the Department of Mathematics of the University of Madras into one of its Centres of Advanced Study. Dr.A.Lakshmanaswamy Mudaliar, Vice Chancellor of University of Madras, welcomed this proposal with enthusiasm. Hence in 1967 these two institutions were amalgamated to form the UGC Centre for Advanced Study in Mathematics and named as the Ramanujan Institute for Advanced Study in Mathematics (RIASM). The UGC took into consideration the significant research record of the two institutions while establishing the RIASM. The UGC sanctioned a sum of Rs.14.40 as non-recurring grant and Rs.29,19,514 as recurring grant for the period 1968-1978.

Prof. C.T.Rajagopal was appointed the Director of the Ramanujan Institute for Advanced Study in Mathematics and when he retired in 1969, the reins were taken over by Dr. T.S.Bhanumurthy. He was the Director till October 1975 and Dr.V.K.Balachandran from October 1975 to October 1977.

Generous funds were made available by the UGC; faculty positions were created and scholarships were also awarded. There were 4 senior fellowships, 6 junior fellowships and 2 post graduate research scholarships granted exclusively to the Center when it was started in 1967. Quite a few of the present faculty of the Institute had benefited by these fellowships during their early days of research.

A new building to house the Institute was constructed in Wallajah Road, Chepauk and was occupied from 3rd October 1972. It was opened by the then Chief Minister Mr. M. Karunanidhi. The present Ramanujan Institute owes its growth to the vision and far-reaching policies of the UGC and the positive attitude of Professor N.D.Sundaravadivelu, the then Vice Chancellor, University of Madras. The new building, where Ramanujan Institute for Advanced Study in Mathematics is still functioning, was located on a plot of more than 3 acres donated by the Government of Tamilnadu and it had 14 rooms in the first wing, 2 Seminar Halls, 18 rooms in the back wing, 1 Library block and 2 Lecture Halls.

A large grant was made towards creating the library of the Institute. It is to be noted that an import license for Rs.25,000/- was obtained to enable the Institute procure lecture notes, seminar and conference reports from abroad. UNESCO dollar coupons were utilized for the purpose. The Institute library is one the finest of its kind in India. The premises of the Library also houses, till today, the collection of books and Journals of the Indian Mathematical Society Library, for which the Director of the Institute acts as the honorary Librarian. It not only serves the needs of the mathematicians in and around the city of Chennai but also those of the researchers from other parts of the country especially the southern states. The University of Madras has supported the Library over the years. Grants have been received from the National Board for Higher Mathematics and the DST under the FIST Program in addition to the amount sanctioned under the SAP Program of the UGC.

During this period 1967-1977, every year the Institute had conducted courses for research scholars and visiting college teachers in the basic areas of Mathematics viz., Analysis, Algebra and Topology. Summer Science Institutes were organized; Special lectures were given and a Colloquium on Riemann Surfaces was conducted.

The staff members at that time focused their research activities on Orders in Cayley and alternative algebras, universal algebras, modular representation of finite Chevelley groups, Tauberian theorems, vector lattice valued measures, complex manifolds and deformations, Kahler manifolds, harmonic spaces, symmetric spaces, Representation of semi-simple Lie groups, Automorphic functions, Differential geometry of Lie groups and their homogeneous spaces, Lattice theory and semigroups, finite groups, Univalent and multivalent functions, Banach spaces of Analytic functions and Riemann surfaces, Modern Summability theory, Non-Archimedean Analysis, Functional Analysis and Operator Theory and Lie Algebras.

Centre had the privilege of Exchange Programmes through which eminent mathematicians spent long, fruitful periods in the Institute. Under "UK Scientific collaboration" distinguished Professors like R.A.Rankin, I.G.Macdonald, J.M. Anderson, R.L.E. Schwarzenberger, K.D.Elworthy, D.Rees, George Lusztig and I.M.James visited the Ramanujan Institute and stayed for a minimum period of 3 weeks each.

"Tata Institute Scientific Collaboration" also was there under which Professors K.Ramachandra, M.S.Raghunathan, C.S.Seshadri, S.Ramanan, K.Varadarajan, S. Raghavan and R.Sridharan visited the Institute and spent not less than a month each in the Institute.

Prof. S.Chandrasekar who was one of the keyfigures in the formation of the center, visited the Institute in Nov. 1968 and April 1971.

It was the visit of Prof. Andre Weil, Institute for Advanced Study, Princeton, New Jersey, USA that paved the way for Ramanujan Institute to establish scientific contact with the Institute for Advanced Study in Princeton.

Other leading mathematicians who visited the Institute during this period include Professors N.Jacobson, R.Ranga rao, M.S.Ramanujan, B.J.Birch, Hyman Bass, M.V.Subba rao, S.R.S.Varadhan, Anthony Zygmund, Harish Chandra and Armand Borel whose visit initiated new areas of research in the Institute. The Institute also published the Lecture Notes of visiting mathematicians as the Publications of the Ramanujan Institute.

Under the various exchange programmmes, Professors Bhama Srinivasan, V.K.Balachandran, K.S.Padmanabhan, G.Rangan, T.S.Bhanumurthy, P.S.Rema, Iqbal Unnisa, T.V.Panchapakesan and S.Sribala visited universities in USA, UK and the Tata Institute of fundamental Research, Mumbai for periods ranging from 2 months to 2 years. The outputs were published in leading international journals. The Institute had established contacts with international centres of mathematical learning, particularly with the Universities of Oxford, Cambridge and Warwick in U.K. and Institute of Advanced Study, Princeton, New Jersey, USA.

Though at its inception the Institute was meant to devote itself solely to advanced research and Ph.D.Programmes, in 1976-77, two full time teaching courses in the Institute viz., M.Sc. Mathematics (I-A) and M.Phil. (Br-I), which are being run successfully till today, were introduced. A good part of the time was taken up in the effective organization and running of these courses which involved besides formal lectures, seminars and discussion classes. The Institute extended help to its sister Departments of Economics, Statistics and Zoology in their teaching programmes by running for them the following courses (i) Mathematical Economics (ii) Analysis and Functional Analysis (iii) Bio-mathematics. It also extended help to the Stella Maris College by running the elective course in Algebraic topology for the M.Sc. During this year a scheme to impart modern mathematics to school teachers was also evolved.

1978-1984

Dr.K.S.Padmanabhan was the Director of the Institute from Oct. 1977 to June 1980 and Dr. T.S.Bhanumurthy was the Director from July 1980 to June 1986.

The Centre had 5 Professors, 3 Readers, 6 Lecturers, 2 Research Associates and 1 Research Assistant during this period.

A new M.Sc. Course called M.Sc. Applicable Sciences was introduced in 1982 and was continued till 1985.

Intensive Research was carried out in the following topics : Orders in Cayley and alternative algebras, Semi groups, universal algebras, modular representation of finite Chevalley groups, univalent functions, Tauberian Theorem, non-archimedean Banach algebras, vector Lattice valued measures, complex manifolds and deformation, Kahler manifolds, harmonic spaces, Symmetric spaces etc.,

1984-1989

During this period an amount of Rs.21 lakhs was sanctioned to the Center by UGC. Further the UGC selected the Institute for funding under the COSIST Programme and sanctioned Rs.8 lakhs.

Three more Lecturer posts were sanctioned to the Institute by UGC under VII Plan.

From July 1986 to June 1987 Dr. V.K.Balachandran was the Director to be followed by Dr. K.S.Padmanabhan till June 1990.

In 1988, Ramanujan Centenary Celebrations were held. Efforts were taken to establish Ramanujan Museum. A special issue of the Journal of Madras University-Part B-Science was dedicated to the Ramanujan Centenary Celebrations. A computer laboratory in the Ramanujan Institute was named as Srinivasa Ramanujan Centenary Computer Centre.

The research areas of the Institute during this period were Lie Algebras, Jordan Algebras and Functional analytic methods in Algebra, Non-archimedean analysis, Tauberian theory, Topological groups, Functional analysis, Kac-Moody Algebras, Algebraic Semigrouops, Coding Theory, Approximation theory, Univalent functions, Ring theory, Representation theory of finite groups, Harmonic Analysis, Optimization, Differential geometry, Potential theory, Semigroups and Probability Theory and Stochastic processes.

A project on L* algebras and Kac-Moody algebras was approved by the UGC and was sanctioned to Dr.V.K.Balachandran.

1989-1992

In July 1990 Dr. Iqbalunnisa succeeded Dr.K.S.Padmanabhan as Director of the Institute. Dr.P.S.Rema became the Director in Dec. 1990 and continued till her retirement in June 1996.

During 1989 - 1990 the UGC Academic Staff College, University of Madras started organizing Refresher Courses in Mathematics for College teachers and the Institute contributed tremendously over the years by conducting more than 15 Refresher Courses in all branches of Mathematics. A number of source books were also published based on the courses.

Dr.M.S.Rangachari was the Co-ordinator for the UGC Curriculum Development Scheme during this period. He was also awarded INSA Project on Editing "Sadaratnamala".

It was decided to organize a symposium every year, National or International, in the Institute named after the luminary Srinivasa Ramanujan. Consequently, the first Ramanujan Symposium was conducted in January 1992 and March 2005 witnessed the conduct of the Twelfth Ramanujan Symposium. Proceedings of these Symposia have also been published.

The faculty members were carrying out research in various topics in Algebra, Analysis, Geometry, Probability and Stochastic Processes, Differential Equations. Research seminars, conferences, national seminars and symposia were organized.

A UGC research project on "Study of extremal problems in the theory of univalent and multivalent functions" was sanctioned to Dr.K.S.Padmanabhan.

Dr.R.Parvatham was sanctioned TWAS research project.

1992-1997

The Institute was recognized as UGC-SAP(CAS Level - Phase I) for the period 1992-1997 and an amount of Rs. 15.75 lakhs was sanctioned.

Dr.M.S.Rangachari succeeded Dr.P.S.Rema as the Director of the Institute in July 1996 and continued till his retirement in June 1998.

The year 1992 - 1993 was of special significance; Ramanujan Institute for Advanced in Mathematics completed 25 years as a UGC centre for Advanced Study. An exclusive Silver Jubilee Lecture was organized on 22 February, 1993. It was delivered by Prof.W.Kohnen, an eminent number theorist from Max Planck Institute, Bonn, Germany on Jacobi forms and Siegel modular forms. A Special Symposium on Approximation theory and its Applications was also organized during 25 - 31, March 1993.

A study seminar on "von Neumann algebras" was also conducted by some faculty members of the Institute. Lectures were given on various topics in von Neumann algebra. Research scholars of the Institute also took an active part in the study seminar. Prof. V.S.Sunder, Institute of Mathematical Sciences, Chennai gave lecturers "On recent developments in von Neumann algebra". This course was very useful to continue this topic as a research field in the Institute.

As a mark of respect to Prof. R.Vaidyanathaswamy, the first Head of the Department of Mathematics, University of Madras, a colloquium called Prof.R.Vaidyanathaswamy Centennial Colloquium was organized by the Institute during December 7 - 8 ,1994 to mark the centenary of Prof.R.Vaidyanathaswamy.

Inspired by the work done in the Institute, an endowment was instituted by Mr.Vittal Rajan in memory of his father Mr. Srinivasa Rajan and the endowment lectures are held every year in January from 1996 till today. The first lecture was delivered by Prof. Waldschmidt, CNRS, Paris, France on 10 January 1996.

A big attraction to anybody inclined towards mathematics is the Mathematical laboratory in the Institute consisting of 65 Mathematical Models. These were purchased with the help of Vikram A.Sarabhai Community Science Centre, Ahmedabad with the "UGC Special Assistance for equipment under VII plan".

A Project on Kocher - Tits Lie algebra of an infinite dimensional Jordan Algebra was sanctioned to Dr.P.S.Rema

A minor research project entitled "Applications of Lie groups to Differential equations - Investigation on generalized symmetries and conservation laws" for a period of 2 years from 11-3-93 to 10-3-95 was sanctioned by UGC to N.Sthanumoorthy.

1998 - 2006

The Institute was recognized as UGC-SAP( CAS Level-Phase II) center and an amount of Rs.22.5 lakhs was sanctioned for the period 1998-2003. An amount of Rs. 8.5 lakhs was sanctioned to the Institute under the X Plan for 2003-2008 and another Rs.16 lakhs under FIST Programme of the DST for 2004-2009. Based on the academic work transacted since the inception and in particular during the Phase II, the Institute is being recognized as UGC-SAP(CAS Level - Phase III) center for the period 2004-2009 under which an amount Rs. 59.99 lakhs has been sanctioned. The Government of Tamilnadu sanctioned Rs. 2 lakhs towards a Project on Mathematical Vocabulary in Tamil to the Institute.

A major research project entitled "Formation of Soliton equations and Solutions for Kac-Moody Lie Algerbas" was sanctioned by DST for a duration of 4 years from 8-9-97 to 7-9-2001 to Dr. N.Sthanumoorthy.

A project on "Continuous symmetries of discrete systems" was sanctioned to Dr.R.Sahadevan by DST to the tune of Rs. 3,40,600/- for the period of 1-3-98 to 28-2-01

A project on Signed Brauer Algebras, Hecke Algebras and their generalizations was approved by UGC and an amount Rs.2,25,560/- was sanctioned to Dr.S.Parvathi A project on Valuations over Composition Algebras and Jordan Algebras was approved by UGC and an amount of Rs.2,76,000/- was sanctioned to Dr.S.Sribala.

Dr.S.Sribala was the Director of the Institute for the period 1998-2002 and Dr.S.Parvathi succeeded her and is continuing as the Director and Head from 2002-date.

Noteworthy changes in the courses offered by the Institute were made during this period. Credit based Semester System was introduced in M.Sc. and M.Phil Courses in 1998 and was further changed to Choice based Credit System in 2000. As a result faculty members of the Institute are offering a number of inter disciplinary courses to the other Departments of the University also. In recent times courses involving practical experience on the computer have also been introduced keeping in mind current international trends in mathematical study.

Two years of this period viz. 2000 and 2002 were of great significance to the Institute. The year 2000, observed as the World Mathematical Year, witnessed a number of research activities. A special issue of the Journal of Madras University-Part B - Sciences was brought out by the Institute. A year long celebration was held by organizing Ramanujan Symposium on Potential Theory and Function Theory, National Conference on Optimization Techniques in Industrial Mathematics and Fifteenth Annual Conference of the Ramanujan Mathematical Society.

The year 2002 marked the Platinum Jubilee of the Department of Mathematics, University of Madras. To commemorate this, a Platinum Jubilee Workshop along with the Ramanujan Symposium on Wavelet Analysis was conducted. During the period 2000-2003, Institutional and Instructional Programmes in Modern Topics like Quantum Groups, Actuarial Mathematics and Discrete Mathematics and International Conference on Kac-Moody Lie Algebras were conducted. The proceedings of the International Conference was published by the Contemporary Mathematics Series of American Mathematical Society. An International Conference on "Non-Commutative Rings, Group Rings, Diagram Algebras and their Applications" was organized in collaboration with Ohio University, Athens, USA.

A grant of Rs.2.lakh by the National Board for Higher Mathematics, Rs. 1 lakh by the The Hindu (Daily Newspaper) and Rs.9 lakh by the Ministry of Culture and Tourism, and a matching grant of Rs. 9 lakh by the University of Madras were sanctioned. The amount was utilized towards establishing the Ramanujan Museum, now housed in the premises of the Ramanujan Institute for Advanced Study in Mathematics, University of Madras.

Utilising the grants from UGC, DST and X Plan, modernization of library, networking facilities and establishment of Computational Mathematical Laboratory-I and II were carried out. AWARDS AND HONOURS F.N.I.: Fellow of National Institute of Science, India 1964: C.T. Rajagopal Nimkar Award to Physically Handicapped : 1993-94: R. Parvatham ISCA Young Scientist Award, 1995: S. Sampathkumar Fellow of National Academy of Sciences, Allahabad, 2000: Geetha Srinivasa Rao Decennial Award by Welfare Foundation of the Blind, 2001: Sushma Agrawal Tamilnadu Scientist Award, 2002: R.Sahadevan Gold Medal, 2002, All India Confederation of Blind: Sushma Agrawal. RAMANUJAN MUSEUM AND RESEARCH CENTRE Under the scheme "UGC Special Assistance for equipment under VII plan", Rs.1 lakh was allotted to the Institute to "strengthen under-graduate and post-graduate laboratories". With the help of the Vikram A. Sarabhai Community Science Centre (VSSC), Ahmedabad a "Mathematical Laboratory", was established to form a part of the proposed RAMANUJAN MUSEUM within the premises of the Institute. About 65 mathematical models were purchased. Two faculty members Dr.M.Loganathan and Dr.V.Thangaraj underwent a training programme on the use and handling of these models at the VSSC. These models were exhibited for the participants of several Refresher Courses conducted through the Academic Staff College of the University of Madras, at the Silver Jubliee conference of the Association of Mathematics Teachers of India held at Madras during January 10-13, 1991 and the Science Exhibition held at Regional Engineering College, Tiruchirapalli during July 10-14,1991 and are being lent to be exhibited by several schools in and around Chennai.

Later on a grant of Rs.2.lakh by the National Board for Higher Mathematics, Rs. 1 lakh by the The Hindu (Daily Newspaper) and Rs.9 lakh by the Ministry of Culture and Tourism, and a matching grant of Rs. 9 lakh by the University of Madras were sanctioned. The amount was utilized towards establishing the Ramanujan Museum, now housed in the premises of the Ramanujan Institute for Advanced Study in Mathematics, University of Madras. A grant of One Crore was sanctioned by the Ministry of Human Resource Development towards the establishment of Ramanujan Museum and Research Centre.

Project on Touch Screen Kiosk at the Ramanujan Institute for the Ramanujan Museum at the Ramanujan Institute is sanctioned by DST. Four units of Touch Screen Kiosk have been purchased under this project.