Nagy János: The Alon-Jaeger-Tarsi conjecture via group ring identities

Abstract:

We prove the Alon-Jaeger-Tarsi conjecture for sufficiently large primes.
Namely, we show that for any finite field $\mathbb{F}$ of size $61<|\mathbb F|\ne 79$ and any nonsingular  matrix $M$ over $\mathbb{F}$ there exists a vector $x$ such that neither $x$ nor $Mx$ has a 0 component.
For this we use a combination of the polynomial method, and different versions of the group ring method and connections between them.
Joint work with Péter Pál Pach.

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