Title: Model theory of multilinear forms
Abstract: Generalizing (and correcting) some work of Granger in the case n=2, we establish a relative quantifier elimination result for non-degenerate n-linear forms and demonstrate that they are NSOP1, and n-dependent assuming that the field is NIP. The latter relies in particular on a higher arity version of the Composition Lemma: a composition of a relation definable in an NIP structure with arbitrary n-ary functions is n-dependent. We also discuss connected components G^{00} and G^{\infty} of definable groups in these examples, and in general n-dependent theories.