Discrete mathematics

Speaker: 
Ilya Shkredov
Speaker Affiliation: 
Steklov Mathematical Institute

April 18, 2023

ESB 4127
Canada

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Abstract: 

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. 

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