# Forbidden vector-valued intersections

• Eoin Long (University of Oxford)
• Thursday 26 January 2017, 14:30-15:30
• MR12.

Given vectors V = (v_i: i \in [n]) in R^D, we define the V-intersection of A,B \subset [n] to be the vector sum_{i \in A \cap B} v_i. In this talk I will discuss a new, essentially optimal, supersaturation theorem for V-intersections, which can be roughly stated as saying that any large family of sets contains many pairs (A,B) with V-intersection w, for a wide range of V and w. A famous theorem of Frankl and Rödl corresponds to the case D=1 and all v_i=1 of our theorem. The case D=2 and v_i=(1,i) solves a conjecture of Kalai.

Joint work with Peter Keevash.

This talk is part of the Combinatorics Seminar series.