HSE University Project Wins Russian-Indian Grant by RSF

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The research community gave a highly positive assessment of a joint application by researchers from HSE University and their Indian colleagues in affine algebraic geometry, particularly the problems of cancellation. The head of the project on the Russian side is HSE FCS Dean Ivan Arzhantsev; on the Indian side, the project is led by renowned mathematician Neena Gupta.

The competition was organized by the Russian Science Foundation (RSF) together with the Department of Science and Technology of the Ministry of Science and Technology of the Republic of India (DST). The grant for 2022–2024 was won by the project entitled ‘Studies on affine spaces and related objects through algebraic group actions and locally nilpotent derivations’, which was presented by HSE University researchers together with their Indian colleagues.

Ivan Arzhantsev, Dean of the HSE Faculty of Computer Science, Project Head

The cancellation problem seems like a natural and a simple issue at the first glance. Let’s look at affine algebraic manifold X, which means a variety of solutions for a system of polynomial equations with many variables over a field of complex numbers. Let’s assume that after adding one more coordinate, or—in geometry language—after multiplying the manifold X by the affine line, we get a manifold that is isomorphic to affine space of n+1 dimension. Is it true that the manifold X is isomorphic to affine space of n dimension? It is known that this is true in the event that X is a curve or a surface. But starting from dimension 3, the question remains open. Neena Gupta managed to build a counterexample to this assertion at n=3, not over a field of complex numbers, but over an arbitrary field, which is an extension of a residue field on a simple module p. It is a very deep result, and to get it, development of an original technique was required.

In the project, we will continue working on the problem of cancellation and on other open problems from affine algebraic geometry, including the problem of linearization. The chance to carry out research together with Indian colleagues opens some completely new opportunities to our research team.

The head of the Indian part is Neena Gupta, a distinguished mathematician who serves as a professor at the Indian Statistical Institute (ISI) in Calcutta. In 2021, she won the Ramanujan Prize (which was first awarded in 2005) for her research in algebraic geometry and commutative algebra. Neena Gupta became the third woman to receive this award. She is known for suggesting a solution for the cancellation problem for affine spaces in positive characteristic.

Earlier, Neena Gupta also received India’s highest prize in science and technology—the Shanti Swarup Bhatnagar Prize—in 2019 in the field of mathematics. In addition, Neena Gupta will speak at the International Congress of Mathematicians, which will take place from July 6-14, 2022.

Neena Gupta

I am happy to be able to implement this project. I am looking forward to more successful joint projects that will come about as a result of this work. We hope to make our contribution to affine algebraic geometry.

The HSE University project has also attracted Amartya Kumar Dutta, a renowned Indian mathematician and professor in the Theoretical Statistics and Mathematics Unit at the Indian Statistical Institute, Calcutta. In 1994, he received his doctorate degree from the University of Mumbai. He proved deep results in affine bundle theory and linear planes over discrete valuation rings. In 2018, Amartya Kumar Dutta received the INSA Best Teachers Award and the Bhatnagar Prize by the Indian Mathematical Society for the best paper on history of mathematics.

Nikhilesh Dasgupta, an international postdoc researcher at the HSE Laboratory on Algebraic Transformation Groups, also entered the Indian project team and played an important role in preparing the joint application.

As part of the international RSF competition, fundamental and exploratory research in the following areas was suggested: Mathematics, Computers and Systems Sciences, Physics and Space Sciences, Chemistry and Materials Science, Biology and Life Sciences, Basic Research for Medicine, Agricultural Sciences, Earth Sciences, and Engineering Sciences.

Russian and Indian experts came together to choose the winners who will receive the grant in the near future. The projects will be implemented in 2022–2024. The size of one RSF grant will be from four to seven million roubles annually.