Discrete mathematics

Ilya Shkredov
Speaker Affiliation: 
Steklov Mathematical Institute

April 18, 2023

ESB 4127

View All Events


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 $\Gamma$ the sequence $|n\Gamma|$  grows very fast. Also, we obtain a series of applications to the sum--product phenomenon and to the Balog--Wooley decomposition--type results. 

Event Topic: