### The Alon-Jaeger-Tarsi conjecture via group ring identities

Combinatorics Seminar

12th October 2021, 11:00 am – 12:00 pm

Virtual (online) Zoom seminar; a link will be sent to the Bristol Combinatorics Seminar and Bristol Number Theory Seminar mailing lists, the week before the seminar.

We prove the Alon-Jaeger-Tarsi conjecture for sufficiently large primes. Namely, we show that for any finite field F of size greater than 61 and not equal to 79, and any nonsingular matrix M over F, there exists a vector x such that neither x nor Mx has a zero component. For this we use a combination of the polynomial method, and different versions of the group ring method and connections between them.

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