Sergei Vladimirovich Konyagin is a plenary speaker, a chief scientific researcher at the Steklov Mathematical Institute of Russian Academy of Sciences.
Sergei received his Ph.D. degree from Moscow State University in 1982 and his Dr. Sc. degree in 1989 also from MSU. He is a full member of Russian Academy of Sciences, a prominent specialist in Harmonic Analysis, Theory of Functions, Number Theory. Konyagin solved well known Littlewood Conjecture on estimation from below of exponential sums, long-standing Lusin problem on the representation of the function by a convergent trigonometric series, and recently he, jointly with K. Ford, B. Green, J. Maynard, and T. Tao, obtained some results in number theory related to long gaps between primes. Konyagin was awarded the Salem Prize, Vinogradov Prize of Russian Academy of Sciences. In 2012 he became a fellow of the American Мathematical Society.
Convergence to Zero of Exponential Sums with Positive Integer Coefficients and Approximation by Sums of Shifts of a Single Function on the Line
(joint work with P.A.Borodin)
We prove that there is a sequence of trigonometric polynomials with positive integer coefficients, which converges to zero almost everywhere. We also prove that there is a functionsuch that the sums of its shifts are dense in all real spaces for and also in the real space .