Annamalai Ramanathan (29 August 1946 – 12 March 1993) was an Indian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

in the field of

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, who introduced the notion of Frobenius splitting of algebraic varieties jointly with

Vikram Bhagvandas Mehta Vikram Bhagvandas Mehta (August 15, 1946 – June 4, 2014) was an Indian mathematician who worked on algebraic geometry and vector bundles. Together with Annamalai Ramanathan he introduced the notion of Frobenius split varieties, which led ...

in . The notion of Frobenius splitting led to the solution of many classical problems, in particular a proof of the

Demazure character formula In mathematics, a Demazure module, introduced by , is a submodule of a finite-dimensional representation generated by an extremal weight space under the action of a Borel subalgebra. The Demazure character formula, introduced by , gives the charac ...

and results on the equations defining

Schubert varieties In algebraic geometry, a Schubert variety is a certain subvariety of a Grassmannian, usually with singular points. Like a Grassmannian, it is a kind of moduli space, whose points correspond to certain kinds of subspaces ''V'', specified using linea ...

in general flag manifolds.

Research career

Ramanathan got his B.Sc in Mathematics at

Ramakrishna Mission Vivekananda College Ramakrishna Mission Vivekananda College, named after Swami Vivekananda, was formally inaugurated on 21 June 1946 by professor, philosopher, and politician, Sarvepalli Radhakrishnan. It is in Mylapore, the centre of Chennai, India, on 20 acres (81 ...

, and was recruited to attend

TIFR Tata Institute of Fundamental Research (TIFR) is a public deemed research university located in Mumbai, India that is dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the De ...

, where he got his Ph.D. in Mathematics in 1976. His thesis on moduli for principal bundles was published in 1996 in two papers in Proc. Indian Acad. Sci. three years after his death. Ramanathan, was a Professor of Mathematics at the

in Bombay, India. He has also been employed at

University of Bonn The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine U ...

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hem ...

and

University of Illinois at Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univ ...

. Ramanathan made significant contributions to many areas of mathematics, including moduli of vector bundles,

Gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups) ...

, algebraic geometry in positive characteristic and

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

Awards

The

Council of Scientific and Industrial Research The Council of Scientific and Industrial Research (IAST: ''vaigyanik tathā audyogik anusandhāna pariṣada''), abbreviated as CSIR, was established by the Government of India in September 1942 as an autonomous body that has emerged as the l ...

awarded he and his collaborator

the

Shanti Swarup Bhatnagar Prize for Science and Technology The Shanti Swarup Bhatnagar Prize for Science and Technology (SSB) is a science award in India given annually by the Council of Scientific and Industrial Research (CSIR) for notable and outstanding research, Applied science, applied or Fundamenta ...

(the Indian Presidential award for achievement in the mathematical sciences) in 1991 for his work in algebraic geometry.

Personal life

Ramanathan was third of four children born to a

Tamil Tamil may refer to: * Tamils, an ethnic group native to India and some other parts of Asia ** Sri Lankan Tamils, Tamil people native to Sri Lanka also called ilankai tamils **Tamil Malaysians, Tamil people native to Malaysia * Tamil language, nati ...

family S. RM. CT. Annamalai and Lakshmi. Ramanathan was crippled by adult onset polio in his late teens, and he used a crutch for the rest of his life. During his tenure as a visiting professor at

, Ramanathan died in

Chicago (''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name ...

, Friday, 12 March 1993, of complications following treatment for a heart attack. He is survived by his wife RM. Vasantha and three daughters Lakshmi Valli Priya.Obituary posted online, at sci.math.research, https://groups.google.com/forum/?fromgroups#!searchin/sci.math.research/annamalai$20ramanathan$20dies/sci.math.research/gjq0hyMv1K4/fXGU-BNWsP4J%5B1-25%5D

Sources

* *

External links

Annamalai Ramanathan
citation

References

{{DEFAULTSORT:Ramanathan, Annamalai 20th-century Indian mathematicians 1993 deaths 1949 births Tata Institute of Fundamental Research alumni Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science