UBC Discrete Math Seminar: Ilya Shkredov

  • Date: 04/18/2023
  • Time: 16:00
Ilya Shkredov, Steklov Mathematical Institute

University of British Columbia


Additive dimension and the growth of sets


We develop the theory of the additive dimension dim(A), i.e. the size of a maximal dissociated subset of a set A. It was shown that the additive dimension is closely connected with the growth of higher sumsets nA of our set A. We apply this approach to demonstrate that for any small multiplicative subgroup Γ the sequence |nΓ| grows very fast. Also, we obtain a series of applications to the sum--product phenomenon and to the Balog--Wooley decomposition--type results.

Other Information: 

Location: ESB 4127

Time: 4pm Pacific