## Speaker:

Ji Zeng

## Speaker Link:

## Institution:

UCSD

## Time:

Wednesday, March 6, 2024 - 2:00pm to 3:00pm

## Host:

## Location:

510R Rowland Hall

The famous no-three-in-line problem by Dudeney more than a century ago asks whether one can select $2n$ points from the grid $[n]^2$ such that no three are collinear. We present two results related to this problem. First, we give a non-trivial upper bound for the maximum size of a set in $[n]^4$ such that no four are coplanar. Second, we characterize the behavior of the maximum size of a subset such that no three are collinear in a random set of $\mathbb{F}_q^2$, that is, the plane over the finite field of order $q$. We discuss their proofs and related open problems.