Braces are algebraic objects introduced by W. Rump in 2007 to help the study of non-degenerate, involutive, set theoretic solutions to the Yang-Baxter equation. Braces have been linked to many other objects of interest - Hopf-Galois extensions, braid groups, quantum groups, trusses, etc. In this talk we focus on the connection between braces and pre-Lie rings. It has been shown that nilpotent pre-Lie rings of cardinality p^n correspond to strongly nilpotent braces of the same cardinality, for sufficiently large primes p. These braces are explicitly obtained from the corresponding pre-Lie rings by the construction of the group of flows. In this talk we introduce braces and pre-Lie rings, and describe the passage between them. As an application we describe how this connection is leveraged for the classification of braces of cardinality p^4.
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