Speaker
Nickolaii Russkin
Description
The family ${D_1,..., D_s}$ is called a sunflower of size s and with kernel $C$, if $D_i \cap D_j = C$ holds for all $1\leq i < j \leq s$ (we assume also $D_i \neq D_j$).
For $r\geq1, \mathcal{F}$ - r-spread, if $|\mathcal{F}(X)|\leq r^{-|X|}|\mathcal{F}|, \forall X \subset [n]$, where $\mathcal{F}(S):=\{A\backslash S:A\in\mathcal{F}, S\subset A\}$
The idea of our work is to construct spread approximation (such a small r-spread (for some r) hypergraph of low uniformity that most of the edges of the original graph contain at least one of its edges) of family and to estimate the maximum size of a sunflower-free family via this approximation and its reminder
