Monday, May 2nd, 2016 | 4pm-5pm | Burnside 1205 |

McGill University

A characterization of functions with vanishing averages over products of disjoint sets.

Given \alpha_1, ..., \alpha_m \in (0,1), we characterize all integrable functions f: [0,1]^m -> \mathbb{C} satisfying \int_{A_1 \times ... \times A_m} f = 0 for any collection of disjoint measurable sets A_1, ...., A_m \subseteq [0,1] of respective measures \alpha_1, ...., \alpha_m. We use this characterization to settle some of the conjectures in [S. Janson and V. Sos, More on quasi-random graphs, subgraph counts and graph limits] about the relation between subgraph counts and quasi-randomness of graph sequences. This is a joint work with Hamed Hatami and Pooya Hatami.