Shkredov, Ilya Dmitrievich

I. D. Shkredov was born in 1980 in the village. (now mountains. ) Golitsyno, Moscow Region . After graduating from the ninth grade of Cuban secondary school No. 2, he moved to the SSC of Moscow State University , and in 1997 he entered the Faculty of Mechanics and Mathematics of Moscow State University (mechmath of Moscow State University).

As a student, since 1999, he began research work under the direction of N. G. Moshchevitin , choosing number theory as his specialization. In 2002 he graduated with honors from Moscow State University. Then he was accepted to the postgraduate study of mechmath, where he wrote a dissertation “On some problems of ergodic number theory” (2005). Since 2006, he has been working at the Department of Dynamic Systems Theory of Moscow State University: until 2010, as an assistant, in 2010, as an assistant professor, and then as a professor . In 2009, he received a doctorate in physical and mathematical sciences , defending his thesis "Combinatorial Properties of High Density Numerical Sets and Their Applications".

Since 2010, she has been a leading researcher at the Department of Number Theory of Steklov Mathematical Institute ( Moscow ), while working at Moscow State University has become part-time . In 2016, Shkredov was awarded the honorary academic title “ Professor of the Russian Academy of Sciences ”, and in October of the same year he was elected a corresponding member of the Academy.

The professional interests of I. D. Shkredov are combinatorial and ergodic number theory, as well as additive and arithmetic combinatorics . The total number of publications is over 60.

In his scientific works Shkredov

• solved the T. Gowers problem of angles , that is, of a two-dimensional generalization of Roth's theorem on arithmetic progressions [the solution is described in the doctoral dissertation ];
• obtained the most general exact result on the structure of sets of large trigonometric sums [see Proceedings of the Russian Academy of Sciences , 72: 1 (2008), 161-182];
• first presented a specific algebraic equation with a minimum number of terms, solvable for any sufficiently large subsets of a finite field [ Mat. Notes 88: 4 (2010), 626-635];
• developed the method of higher energies, highest sums, and eigenvalues ​​of the corresponding operators , which made it possible to obtain new results in additive combinatorics (structural theorems, estimates of the energies and sums of sets of combinatorial families) and in number theory (an estimate of the Heilbronn trigonometric sum and results on the Fermat quotient distribution [ Quart. J. Math. , 64: 4 (2013), 1221-1230], estimates of trigonometric sums by subgroups [ Finite Fields Appl. , 30 (2014), 72-87]).
• received, together with T. Schoen, the first exact estimate for the density of a set without solving an affine linear equation [ Israel J. Math. 199: 1 (2014), 287-308];
• Together with S.V. Konyagin, he solved, up to a constant in the degree of the logarithm, the problem of J.-P. Kahana on the quantitative form of the Burling-Helson theorem [ Function Anal. & Appl. , 49: 2 (2015), 39-53];
• together with the co-authors received the best results to date in questions of sum-products in the real field and in finite fields [ Proc. of the Steklov Institute of Mathematics , 294 (2016), 87-98; Advances in Mathematics , 293 (2016), 589-605]. It turned out that for these results one can find applications in cryptography ^[3] , theoretical computer science , number theory, and in the field of dynamical systems .

I. D. Shkredov -

• winner of the prize. P. Deligne ^[4] , Balzan Foundation (2007);
• winner of the competition of the President of the Russian Federation ^[5] for candidates of sciences (2006, 2009);
• holder of the honorary academic title “Professor of the Russian Academy of Sciences” ^[1] (2016).

His research work has been repeatedly supported by the RFBR , RSF and other grantors .

In the 2000s, he taught MSU students the course “ Ordinary Differential Equations ” and special courses “Szemeredi’s Theorem and Fourier Analysis”, “Arithmetic Progressions”. He taught at a number of other educational institutions in Moscow ( Independent University , high schools).

In order to popularize scientific knowledge, he collaborates with the Post-Science project, speaking there, in particular, with lectures on combinatorial ergodic theory and about Szemeredi theorem .

Twice, one semester , he was invited to research in the USA : participated in the work of scientific schools “Arithmetic Combinatorics” (2007, Institute for Advanced Study , Princeton ) and “Dynamical Systems and Additive Combinatorics” (2008, English Mathematical Science Research Institute , Berkeley ).

• Information about I. D. Shkredov on the All-Russian Mathematical Portal
• Information in the Truth system about the work of I. D. Shkredov
• Homepage of I. D. Shkredov