Научные интересы включают в себя дискретную и выпуклую геометрию, экстремальную комбинаторику.

В 2013 году защитил кандидатскую диссертацию на механико-математическом факультете МГУ под руководством Юрия Валентиновича Нестеренко.

С октября 2015 по сентябрь 2017 я был постдоком в Технионе под руководством Рома Пинхаси.

В настоящий момент старший научный сотрудник МФТИ.

Подготавливаются к печати

1. M. Naszódi, A. Polyanskii,
   Perron and Frobenius meet Carathéodory, in preparation
2. A.C. Manzano, M. Naszódi, A. Polyanskii,
   Greedy integer programming, in preparation
3. F. Nilov, A. Polyanskii,
   Silvester-Gallai theorem for vectors, in preparation
4. N. Chernega, A. Polyanskii, R. Sadykov,
   Non-crossings in geometric graphs, in preparation

Научно-исследовательские работы

1. Z. Jiang, A. Polyanskii,
   Forbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines, Israel Journal of Mathematics, accepted.
2. A. Polyanskii,
   On almost-equidistant sets - II, The Electronic Journal of Combinatorics, 26 (2) (2019), #P2.14.
3. A. Polyanskii,
   Helly-type theorem for eigenvectors, in preparation
4. A. Polyanskii,
   On simultaneous approximations of $\ln{3}$ and $\frac{\pi}{\sqrt{3}}$ by rational numbers, Sbornik:Mathematics, accepted.
5. A. Polyanskii,
   On almost-equidistant sets, Linear Algebra and its Applications, 563 (2019), 220-230.
6. A. Polyanskii,
   On the irrationality measures of certain numbers-II, Mathematical Notes, 103 (3-4) (2018), 626-634.
7. B.G. Merino, T. Jahn, A. Polyanskii, G. Wachsmuth,
   Hunting for reduced polytopes, Discrete and Computational Geometry, 60 (3) (2018), 801-808.
8. M. Naszódi, A. Polyanskii,
   Approximating set multi-covers, European Journal of Combinatorics, 67 (2018), 174-180.
9. A. Kupavskii, A. Polyanskii,
   Proof of Schur's conjecture in $R^d$, Combinatorica, 37 (6) (2017), 1181-1205.
10. A. Polyanskii,
    Pairwise intersecting homothets of a convex body, Discrete Mathematics, 340 (8) (2017), 1950-1956.
11. Z. Jiang, A. Polyanskii,
    Proof of László Fejes Tóth's zone conjecture, Geometric and Functional Analysis, 27 (6), (2017), 1367–1377.
12. A.B. Kupavskii, A.A. Polyanskii,
    On simplices in diameter graphs in $R^4$, Mathematical Notes, 101(2) (2017), 265-276.
13. V.V. Bulankina, A.B. Kupavskii, A.A. Polyanskii,
    On Schur's conjecture in $R^4$, Mathematical Notes, 97(1) (2015), 21-29.
14. A. Polyanskii,
    On a question of Makai and Martini on bodies of constant width, Contributions to Algebra and Geometry, 55(2) (2014), 635-636.
15. V.V. Bulankina, A.B. Kupavskii, A.A. Polyanskii,
    Note on Schur's conjecture in $R^4$, Doklady Mathematics, 89(1) (2014), 88-91.
16. A. Polyanskii,
    Quadratic irrationality exponents of certain numbers, Moscow University Mathematics Bulletin, 68 (5) (2013), 237-240.
17. A. Polyanskii,
    Square exponent of irrationality of $\ln{2}$, Moscow University Mathematics Bulletin, 67(1) (2012), 25-30.
18. A. Polyanskii,
    On the irrationality measure of certain numbers, Moscow Journal of Combinatorics and Number Theory, 1(4) (2011), 80-90.

Описательные документы

1. A. Polyanskii, P. Tarasov,
   Selected examination problems in Discrete Analysis, Matematicheskoe Prosveschenie (2017), 205-209 (in Russian).
2. F. Nilov, A. Polyanskii, N. Polyanskii
   Szemerédi-Trotter theorem, Matematicheskoe Prosveschenie (2017), 186-196 (in Russian).
3. A. Polyanskii,
   Solving problems without using Pick's formula, Kvant 2 (2013), 40-42 (in Russian).
4. A. Polyanskii,
   To shoot a cannon with sparrows, Kvant 2 (2012), 49-50, 60-61 (in Russian).

Исследовательские проекты для Летней конференции Турнира Городов

1. F. Nilov, A. Polyanskii, N. Polyanskii,
   Point-Line Incidences, (2014), Kaliningrad (bilingual).
2. A. Zaslavskiy, F. Nilov, A. Polyanskii, M. Skopenkov,
   Webs from lines and circles, (2012), Teberda (bilingual).

Кандидатская диссертация

1. A. Polyanskii,
   On the irrationality measure of certain numbers (in Russian), Department of Mechanics and Mathematics of Moscow State University, November 2013.