## University of Sydney Algebra Seminar

# Gyula Karolyi (University of Queensland)

## Friday 15th March, 12:05-12:55pm, Carslaw 373

### Some applications of the Combinatorial Nullstellensatz

The Combinatorial Nullstellensatz, introduced by Noga Alon in his 1999 seminal paper, effectively describes the structure of polynomials that vanish on a Cartesian product. Due to this effectiveness, it has a wide range of applications from finite geometry to combinatorial arithmetic to graph colourings. A recent variant even connects to statistical mechanics and representation theory by allowing us to turn often difficult constant term evaluations into simple combinatorial problems. In this talk, very elementary in nature, I will illustrate the methodology through some examples.