# Turán-Type Theorems for Triangles in Convex Point Sets

## Pat Morin, Carleton University, Ottowa

## April 12, 2016

Originally motivated by a problem of ErdÅ‘s on the maximum number of
maximum-area triangles determined by an n-point set, we will discuss
some new and old results on the following family of problems: Given a
set of n points in convex position, what is the maximum number
triangles one can create having these points as vertices while
avoiding certain sets of forbidden configurations. As forbidden
configurations we consider all 8 ways in which a pair of triangles in
such a point set can interact by sharing and/or interleaving vertices.
We will present old and new results and techniques and open problems.