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, mathematical structure, structure, space, Mathematica ...

in the field of

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, who introduced the notion of

Frobenius splitting In mathematics, a Frobenius splitting, introduced by , is a splitting of the injective morphism O''X''→F*O''X'' from a structure sheaf O''X'' of a characteristic ''p'' > 0 variety ''X'' to its image F*O''X'' under the Frobenius endomorp ...

of algebraic varieties jointly with Vikram Bhagvandas Mehta in . The notion of

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, \mathbf_k(V) of k-dimensional subspaces of a vector space V, usually with singular points. Like the Grassmannian, it is a kind of moduli space, whose elements sati ...

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 leading research Institute under the Department of Atomic Energy of the Government of India. It is a public deemed university located at Navy Nagar, Colaba in Mumbai. It also has a centres in B ...

, 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 University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Willi ...

Johns Hopkins University The Johns Hopkins University (often abbreviated as Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland, United States. Founded in 1876 based on the European research institution model, J ...

and

University of Illinois at Urbana-Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...

. 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 under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...

, algebraic geometry in positive characteristic and

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

Awards

The

Council of Scientific and Industrial Research The Council of Scientific and Industrial Research (CSIR; IAST: ''vaigyanik tathā audyogik anusandhāna pariṣada'') is a research and development (R&D) organisation in India to promote scientific, industrial and economic growth. Headquarter ...

awarded he and his collaborator Vikram Bhagvandas Mehta the

Shanti Swarup Bhatnagar Prize for Science and Technology Shanti or Shanthi may refer to: In Sanskrit * Inner peace, a state of being mentally and spiritually at peace, with enough knowledge and understanding to keep oneself strong in the face of discord or stress * Kshanti, one of the paramitas of B ...

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

Personal life

During his tenure as a visiting professor at

, Ramanathan died in

Chicago Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of Unite ...

, 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 Polio survivors