HSE Scholars Win Young Russian Mathematics Contest
Associate Professor Yulia Zaitseva of the Faculty of Computer Science’s Big Data and Information Retrieval School and Research Assistant Ekaterina Nistyuk of the Laboratory on Algebraic Transformation Groups have been named among the winners of the Young Russian Mathematics research grant competition. Also among the awardees is Vladislav Pokidkin, a PhD student at the Faculty of Mathematics.
Young Russian Mathematics is a competition for students, PhD candidates, and early-career researchers conducting research under the supervision of leading scholars. Its aim is to support talented young scientists working in the field of fundamental mathematics. The competition is organised by the BASIS Foundation and the Independent University of Moscow.
This year, in the category of grants for Candidates and Doctors of Sciences, support was awarded to Yulia Zaitseva’s project ‘The Geometry of Idempotents in Algebraic Monoids.’
In the category PhD student or early-career researcher without a degree, the projects ‘Gelfand–Tsetlin Polytopes and Schubert Calculus’ by Ekaterina Nistyuk and ‘Discriminants of Polynomial Systems and Their Applications’ by Vladislav Pokidkin were recognised.
Vladislav Pokidkin
‘Current research carried out under the supervision of Alexander Esterov focuses on applying discrete mathematics to classical algebraic geometry—more specifically, on describing special algebraic sets, namely discriminants of polynomial systems. The main goal is to enumerate the components, their dimensions, and degrees for discriminants of polynomial systems consisting of n equations in n variables, with no restrictions on the value of n or on the form of the equations,’ Vladislav Pokidkin explained.
As part of her research project, Ekaterina studies the relationship between combinatorial objects such as Gelfand–Tsetlin polytopes and geometric objects—flag varieties of the classical types A, C, and D. In particular, geometric objects known as Schubert cycles can be represented as linear combinations of faces of these polytopes. This correspondence makes it possible to carry out certain geometric computations using only the combinatorics of polytopes.
An explicit correspondence between faces and Schubert cycles for type A flags was described in 2012. The face diagrams obtained in that work resemble pipes from the game Pipe Dream arranged on a triangular grid.
Ekaterina Nistyuk
‘For type C flags, there was no known analogue of the Pipe Dream game, and it took about ten years to generalise this correspondence to type C. This was done by the Japanese mathematician Naoki Fujita. In my recent graduation thesis, I formulated similar conjectures for type D flags. The main aim of the project is to extend the known correspondences established for the classical types A and C to the remaining type D,’ Ekaterina said.
Alexandra Skripchenko
‘Receiving a grant from the BASIS Foundation is, first and foremost, the result of a high-level independent assessment of the quality of research carried out by PhD students,’ noted Alexandra Skripchenko, Dean of the HSE Faculty of Mathematics. ‘The competition jury includes outstanding Russian mathematicians, and this kind of recognition from them is certainly an important motivating factor for our young colleagues.
Such support is extremely important for early-career researchers for many reasons. In addition to the obvious financial and reputational incentives, PhD students gain valuable and disciplining experience in research administration, as well as additional opportunities to talk about the most interesting thing of all—the mathematics they work on—to people who are able to appreciate their achievements.
For HSE University, this kind of high appraisal of our PhD students is a signal that we are moving in the right direction.’
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