# Combinatorics Seminar

When: Sunday, May 22, 10am

Where: Schreiber 309

Speaker: Eoin Long, Tel Aviv U.

Title: Forbidden vector-valued intersections

## Abstract:

Given vectors V = (v_i)_{i\in [n]} in Z^d, we define the V-intersection of A,B \subset [n] to be the vector \sum_{i \in A \cap B} v_i. I will speak about an 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 any given V and w satisfying certain conditions that are in a sense best possible. A famous theorem of Frankl and Rodl 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.

redesigned by barak soreq