Mikhail Gabdullin

Mathematician

University of Illinois Urbana-Champaign, Faculty of Mathematics
gabdullin.mikhail@yandex.ru; mikhailg@illinois.edu

Hello! I am a mathematician working in analytic number theory and harmonic analysis (currently employed in University of Illinois Urbana-Champaign). I am interested in various subjects related to estimates of character sums and their applications, distribution of quadratic residues, distribution of primes, values of arithmetic functions, convergence of trigonometric series, trigonometric polynomials with frequencies in the set of squares.

I have different hobbies. One of them is chess: I am a candidate master (ELO 2207) and was Ural Federal District Champion under 14 (2004). I am also passionate about classical music (in particular, about Beethoven piano sonatas), yoga, and martial arts.

Employment

2023 - present
J.L.Doob Research Assistant Professor (University of Illinois Urbana-Champaign)
2020 - present
Researcher (Steklov Mathematical Institute, Moscow)
2018 - 2023
Researcher (Moscow State University, Laboratory of Multidimensional Approximation and Discretization)
2013 - 2021
Researcher (Institute of Mathematics and Mechanics UrB RAS, Yekaterinburg)

Awards

Young Russian Mathematics winner (2020)
The best paper of Steklov Institute (2020)

Education

Ural State University, Department of Mechanics and Mathematics: B.S. (2013), M.S (2015) in Mathematics;
Moscow State University, Faculty of Mechanics and Mathematics: Ph.D. (2015 - 2019); advisor Sergei Konyagin;
Ph.D. thesis: Estimates of character sums and its applications.

List of my publications

1

Primes with small primitive roots (joint with K. Ford, A. Granville)
2

Long strings of consecutive composite values of polynomials (joint with K. Ford), to appear in Trans. Amer. Math. Soc.
3

Prime avoiding numbers is a basis of order 2, (joint with A. Radomskii), to appear in Sb. Math.
4

Trigonometric polynomials with frequencies in the set of cubes (joint with S. Konyagin), Math. Notes, 115:3 (2024), 337–341
5

Trigonometric polynomials with frequencies in the set of squares and divisors in a short interval, J. Fourier Anal. Appl. 30, 2 (2024)
6

Numbers of the form k+f(k) (joint with V. Iudelevich, F. Luca), J. Number Theory, 262 (2024), 58–85
7

Karatsuba's divisor problem and related questions, (joint with V. Iudelevich, S. Konyagin), Sb. Math., 214:7 (2023), 919–933
8

Numbers of the form kf(k) (joint with V. Iudelevich, F. Luca) Int. J. Number Theory, 19:5 (2023), 1191–1204
9

The stochasticity parameter of quadratic residues, Int. Math. Res. Not. IMRN, (2022), 1–24
10

Trigonometric series with noninteger harmonics, J. Math. Anal. Appl., 508:1 (2022): 125792-11
11

Sets whose differences avoid squares modulo m (joint with K. Ford), Proc. Amer. Math. Soc., 149 (2021), 3669–3682
12

Lower Bounds for the Wiener Norm in Z_p^d, Math. Notes, 107:4 (2020), 574–588
13

Sets in Z_m whose difference sets avoid squares, Sb. Math., 209:11 (2018), 1603–1610
14

Estimates for character sums in finite fields of order p^2 and p^3, Proc. Steklov Inst. Math., 303 (2018), 36–49
15

On divergence of Fourier series in \varphi(L) spaces containing L, Math. Notes, 99(6), 878-886 (2016)
16

On squares in special sets of finite fields, Chebysh. Sb., 17:2 (2016), 56–63
17

On the squares in the set of elements of a finite field with constraints on the coefficients of its basis expansion, Math. Notes, 101(1), 234--249 (2016)
18

On the divergence of trigonometric Fourier series in classes \varphi(L) contained in L, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2015), 81–87
19

An estimate of the geometric mean of the derivative of a polynomial in terms of its uniform norm on a closed interval, Proc. of Krasovskii Inst. of Mathematics and Mechanics UB RAS, 18, № 4, 2012, 153–161 (in Russian)

Visiting Appointments

1

Combinatorial and Additive Number Theory, (05/2023, online)
2

The Second Conference of Russian Mathematical Centers, Moscow
(11/2022)
3

Alfred Renyi Institute of Mathematics, Budapest (07/2022)
4

Number Theory Conference, Debrecen (07/2022)
5

Combinatorial and Additive Number Theory, (05/2022, online)
6

Approximation Theory and Applications (dedicated to the 100th anniversary of S.B. Stechkin) (Moscow, 09/2021)
7

Combinatorial and Additive Number Theory, (05/2021, online)
8

London Number Theory Seminar (invited speaker) (06/2019)
9

Uniform Distribution Theory, CIRM, Marseilles (10/2018)
10

Canadian Number Theory Association Conference, CNTA XV, Quebec (07/2018)
11

Journees Arithmetiques, Caen (07/2017)
12

Mathematical Science Research Institute, Berkeley (01/2017--02/2017)
13

Alfred Renyi Institute of Mathematics, Budapest (07/2016)
14

Uniform Distribution Theory, Sopron (07/2016)
15

Theory of Approximation Fucntions and its Applications, Kamianets-Podilsky (05/2012)

Contact me :)

E-mail: gabdullin.mikhail@yandex.ru
mikhailg@illinois.edu