# Workshop on Additive Combinatorics and Algebraic Connections

## 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 this talk we discuss the proof of this result for primes larger than 61 and mention further applications of our method about coset covers and additive bases. Joint work with János Nagy and István Tomon.

## Date & Time

October 25, 2022 | 4:00pm – 5:00pm

### Location

Simonyi 101 and Remote Access### Speakers

Peter Pach

## Affiliation

Budapest University