Dr Neena Gupta, Associate Professor at the Theoretical Statistics and Mathematics Unit of the Indian Statistical Institute (ISI), Kolkata, has been awarded the Shanti Swarup Bhatnagar Prize 2019, in the field of Mathematical Sciences. This prize, one of the most prestigious awards in the country for research in Science, honours scientists for significant and cumulative contribution to their area of research. Dr Gupta, the youngest person in Mathematical Sciences to receive this award till date, has been recognised for her contributions to affine algebraic geometry, especially in proposing a solution to the Zariski Cancellation Problem.
Elated about winning the award, Dr. Gupta attributes her success to her strong conceptual foundation and the guidance of her teachers.
"Behind a successful person, there are many people, not just one. You need support from the whole system. My parents were very keen on getting me higher education. My PhD supervisor, Prof Amartya Kumar Dutta, has been very encouraging. Also, I am fortunate to have a very supportive husband and in-laws," she shares in an interview with Research Matters.
Dr. Gupta's field of research is Commutative Algebra and Affine Algebraic Geometry. Commutative algebra, apart from being a beautiful subject, provides a base over which a vast body of pure mathematics develops, Algebraic Geometry being one of the primary ones.
A quick recap of high school geometry reminds us of polynomial equations which govern geometric shapes, like x2 + y2 = r2 for a circle or x2/a2 – y2/b2 = 1 for a hyperbola. But these shapes start getting complicated when the number of variables and the number and the degrees of the equations involved increase. Affine Algebraic Geometry, the research area of Dr. Gupta, deals with the understanding of the properties of geometric objects that arise as solutions of systems of polynomial equations. Her natural strength being in Algebra, Dr. Gupta approaches these problems using algebraic methods.
In the last few years, Dr Gupta has provided solutions to two open problems, one of which was posed by Oscar Zariski (1899-1986), one of the founders of modern Algebraic Geometry. She describes these open mathematical conjectures as problems which can be easily explained to mathematicians but are very difficult to solve. The 'Zariski Cancellation Problem' has intrigued mathematicians around the globe, since a version of it was proposed by O. Zariski in 1949.
“The cancellation problem asks that if you have cylinders over two geometric structures, and they have similar forms, can one conclude that the original base structures have similar forms?" explains Dr Gupta.
Another problem solved by Dr. Gupta was posed by Masayoshi Miyanishi, who is now revered as a father figure among the present affine algebraic geometers.
During the later half of the 20th century and early 21st century, eminent mathematicians have tried to work out a solution for the Zariski Cancellation Problem. This particular problem had remained open for about 70 years, before Dr. Gupta finally provided a complete solution to it in positive characteristic, in 2014.
"I knew this problem right from my PhD days, but I never imagined that I will be able to solve it," she says, pleasantly surprised. The solutions provided by Dr Gupta have given both insights and inspiration to young researchers as they can initiate research into other associated conjectures, which remain open.
Till 2019, there have been 547 Bhatnagar awardees, out of which, only 17 are women. "There needs to be social awareness so that people start sending their girl child for higher education," she says in response to the question about gender disparity in the scientific community.
The thrill of solving problems, based on mathematical theories, is her greatest motivation. Ground-breaking results do not come overnight and are a result of patience, perseverance and continuity of efforts put into scientific research.
"Maths is for somebody who can solve the problems on their own. The pleasure which I get in solving problems in mathematics is much more than any award," signs off Dr Gupta.