# Dr. Neena Gupta – The 2021 DST-ICTP-IMU Ramanujan Prize Winner

*Dr Prakash K Sahu, School of Applied Sciences (Mathematics)*

Professor Neena Gupta, a mathematician and professor at the Indian Statistical Institute in Kolkata, has been awarded the 2021 DST-ICTP-IMU Ramanujan Prize for young mathematicians from developing countries. She received the prize for her outstanding work in affine algebraic geometry and commutative algebra, for her solution to the Zariski cancellation problem for affine spaces. She is the fourth Indian to win this prestigious prize.

**The DST-ICTU-IMU Prize**

The DST-ICTU-IMURamanujan Prize was instituted in 2005 for young mathematicians from developing countries and is administered by the Abdus Salam International Centre for Theoretical Physics (ICTP) jointly with the Department of Science and Technology (DST), Government of India, and the International Mathematical Union. The Prize is presented annually to an eminent mathematician who is less than forty-five years of age on December 31 of the year of the Prize and has conducted outstanding research in a developing country. A galaxy of eminent mathematics from around the world comprise the Selection Committee for the Prize. The Committee considers not only the scientific quality of the research in mathematics and the background of the candidate but also the adversities that surround and the work environment of the researcher. The Prize carries a cash award of US$15,000.

Dr. Gupta is the fourth mathematician from India to achieve the distinction of getting the Prize for the year 2021. Before Gupta, Indian mathematicians Ramdorai Sujatha, Amalendu Krishna, and Ritabrata Munshi received the Prize in 2006, 2015, and 2018 respectively.

**Dr. Neena Gupta’s Life and Awards**

Neena Gupta was born in Kolkata in an average Indian family in the year 1984. She completed her bachelor’s degree in mathematics from Bethune College, Kolkata and stood First class First in the Mathematics Honours examination of the Calcutta University in 2006. Dr. Gupta completed her master’s degree in mathematics from the Indian Statistical Institute in the year 2008 and got the Ph. D. degree from the same institute in 2011. Her doctoral work was in the field of Commutative Algebra and she did the work under the supervision of Prof. Amartya Kumar Dutta. The title of her thesis was “Some Results on Laurent Polynomial Fibrations and Quasi A*-Algebras”. During her Ph. D. she was a Shyama Prasad Mukherjee Research Fellow at ISI Kolkata from Sep 2008 to Feb 2012. After brief periods of work at ISI Kolkata as a visiting scientist (Feb–Apr 2012) and at TIFR Mumbai as a visiting fellow (May–Dec 2012), Dr. Gupta became an INSPIRE Faculty at ISI Kolkata in Dec 2012 and is now working as an associate professor at the Statistics and Mathematics Unit of the same institute since then.

Dr. Gupta is the third woman to be awarded the prestigious DST-ICTU-IMU Prize. She of course has been awarded with many honours and distinctions before this award. Dr.. Gupta was honored as TWAS Young Affiliates in 2020 and received the Shanti Swarup Bhatnagar award in 2019 in the field of mathematical sciences, the highest honour given in India in the subject of science and technology. She also received the Swarna Jayanti Fellowship Award by DST, India in 2015 and the INSA Young Scientist award in 2014 for the solution she had proposed to the Zariski Cancellation Problem in positive characteristic. Also, she was honored with the inaugural Professor A. K. Agarwal Award for best research publication by the Indian Mathematical Society in 2014 and Ramanujan Prize from the University of Madras in the same year. Her work on the conjecture also earned her the inaugural Saraswathi Cowsik Medal in 2013, awarded by the TIFR Alumni Association.

**Professor Gupta’s Research**

Prof. 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: *x*^{2} + *y*^{2} = *r*^{2} for a circle or *x*^{2}/*a*^{2} – *y*^{2}/*b*^{2} = 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 to 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 because a version of it was proposed by O. Zariski in 1949.

**Sources**

- https://www.ictp.it/about-ictp/prizes-awards/the-dst-ictp-imu-ramanujan-prize.aspx
- https://en.wikipedia.org/wiki/Neena_Gupta_(mathematician)
- Bhatwadekar, S. M. and N. Gupta (2015), A Note on the Cancellation Property of
*k*[*X*,*Y*], Journal of Algebra and Its Applications, 14 (09), 1540007. - Bhatwadekar, S., N. Gupta, and S. Lokhande (2017), Some
*K*-Theoretical Properties of a Kernel of a Locally Nilpotent Derivation k[X_1,…,X_4] Transactions of the American Mathematical Society, 369 (1), 341–363. - Chakraborty, S., N. Dasgupta, A.K. Dutta, and N. Gupta (2021), Some Results on Retracts of Polynomial Rings, Journal of Algebra, 567, 243–68.
- Dasgupta, N. and N. Gupta (2018), Nice Derivations over Principal Ideal Domains, Journal of Pure and Applied Algebra, 222 (12), 4161–4172.
- Dutta, A. K., N. Gupta, and N. Onoda (2012), Some Patching Results on Algebras over Two-Dimensional Factorial Domains, Journal of Pure and Applied Algebra, 216 (7), 1667–1679.
- Gupta, N. and S. Sen (2020), Locally Nilpotent Derivations of Double Danielewski Surfaces, Journal of Pure and Applied Algebra, 224 (4), 106208.
- Gupta, N. and S. Sen (2019), On Double Danielewski Surfaces and the Cancellation Problem, Journal of Algebra, 533, 25–43.
- Gupta, N. (2015), A Survey on Zariski Cancellation Problem, Indian Journal of Pure And Applied Mathematics, 46 (6), 865–877.
- Gupta, N. (2014), On the Cancellation Problem for the Affine Space in Characteristic , Inventiones Mathematicae, 195 (1), 279–288.
- Gupta, N. (2014), On Zariski’s Cancellation Problem in Positive Characteristic, Advances in Mathematics, 264, 296–307.