The Alon-Jaeger-Tarsi conjecture via group ring identities

Abstract: The Alon-Jaeger-Tarsi conjecture states that for any finite field $F$ of size at least 4 and any nonsingular matrix $M$ over $F$ there exists a vector $x$ such that neither $x$ nor $Mx$ has a 0 component. In joint work with János Nagy we proved this conjecture when the size of the field is sufficiently large, namely, when $61<|F|\ne 79$. In this talk we will discuss this result.

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.