## Number Theory Seminar - Keshia Yap

### Monday, March 16th, 2020

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 422

**Speaker:** Keshia Yap

**Title:** Dimension of magic squares over a field.

**Abstract:** In this talk, we will follow the proof of Charles Small's 1988 paper to compute the dimension of magic squares over fields. A magic square of size $n$ over a field $F$ is an $n \times n$ matrix for which every row, every column, the principal diagonal and the principal backdiagonal all have the same sum. The set of all magic squares is an $F$-vector space. We will prove that for $n \geq 5$, its dimension is $n^2 - 2n$ (for all $F$), and for $n