University of the Philippines Diliman — Institute of Mathematics

Multicomplex numbers extend complex numbers by adjoining several commuting square roots of minus one. William Verreault shows how classifying certain canonical involutions reduces to studying a particular family of involutory matrices in characteristic two, giving an explicit enumeration of the involutions. Returning to analysis, he explains how these involutions define complex structures and corresponding Cauchy–Riemann equations for multicomplex-valued functions. Although the chosen involution changes the coordinates of those equations, the resulting class of holomorphic functions remains unchanged.