Emmy Noether Lecture 2025

Neena Gupta, Indian Statistical Institute

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Professor Neena Gupta, Theoretical Statistics and Mathematics Unit (TSMU-Kolkata), Indian Statistical Institute, is recognized for outstanding contributions to affine algebraic geometry, for creating deep theories and research expository that have attracted many mathematicians to the field, and for being a brilliant problem solver who successfully solved one of the most challenging and longstanding open questions of nearly seven decades – the “Zariski Cancellation Problem.”

The discovery of this bridge is itself a landmark with enormous potential. More broadly, Neena has been making masterly contributions in the area of affine fibrations, including a structure theorem for locally Laurent polynomial algebras, a beautiful analogue of the theorem for locally polynomial algebras due to Bass-Connell-Wright and Suslin. In another landmark paper in Transactions of the AMS (with Bhatwadekar-Lokhande), Neena presents an infinite family of counterexamples to a conjecture of M. Miyanishi on the invariant subring of a polynomial ring under the additive group Ga, a topic closely related to Hilbert’s Fourteenth Problem. 

Further contributions include cancellation property of the affine plane over any field, the discovery of a new class of non-cancellative surfaces (named double Danielewski) and their properties, the triviality of separable affine three-forms under certain hypotheses, results and examples on a question arising out of Zariski’s Theorem on Hilbert’s Fourteenth Problem about finite generation of Noetherian algebras over a two-dimensional regular local ring which are subrings of polynomial rings, results relating “retract of polynomial ring,” “affine fibration,” and “kernel of locally nilpotent derivation,” new algebraic characterizations of the affine plane and the affine three-space.

Gupta has been recognized with a number of high honors, including being invited as an ICM 2022 Sectional Speaker in two sections: Algebra as well as Algebraic and Complex Geometry. In 2019 Neena earned the distinction of being the youngest ever mathematician to be awarded India’s highest scientific honour, the Shanti Swarup Bhatnagar Prize. She received the ICTP Ramanujan Prize in 2021 for “her outstanding work in affine algebraic geometry and commutative algebra, in particular for her solution to the Zariski cancellation problem for affine spaces.”

Neena’s breakthroughs and extraordinarily prolific contributions have been inspiring young researchers in India. Her biography is being published in a book, Vigyan Vidushi (75 women trailblazers in Indian Science) on the occasion of 75 years of Indian independence. The Honourable President of India conferred the 2021 Nari Shakti Puraskar (award for woman empowerment) to Neena on International Women’s Day March 8, 2022. Coincidentally, Gupta has also co-authored a popular article: Emmy Noether: the Mother of Modern Algebra, A.K. Dutta and Neena, written for Lekhon, a publication of ISI Club.