Early Explorations of America, real and imaginary

Working in the real and the imaginary

The science we practice is shaped by our interactions with people; the enthusiastic teachers, the fascinating mentors, the inspiring colleagues, and the inquisitive students. The science we enjoy takes us into areas we couldn't have anticipated. From time to time, we come back to reality and try to find ways to share our new explorations with our friends and relatives and to convert our insight...

Imaginary wars in the wilds of Portuguese America

The southeastern, central and southern areas of Brazil have shared a common regional history ever since the period when they formed part of the Portuguese Empire. From the end of the seventeenth to the twenty-first century, it is possible to identify many contexts and situations of tension, conflict, negotiation and agreement between the various parts of this territory, such as the movement of ...

Imaginary automorphisms on real hyperelliptic curves

A real hyperelliptic curve X is said to be Gaussian if there is an automorphism α : XC → XC such that α = [−1]C ◦ α, where [−1] denotes the hyperelliptic involution on X. Gaussian curves arise naturally in several contexts, for example when one studies real Jacobians. In the present paper we study the properties of Gaussian curves and we describe their moduli spaces. MSC 2000: 14H15, 14H37, 14P...

[Bird flu: a real or imaginary threat?].

A real explanation for imaginary eigenvalues

Abstract This paper first reviews how anti-symmetric matrices in two dimensions yield imaginary eigenvalues and complex eigenvectors. It is shown how this carries on to rotations by means of the Cayley transformation. Then the necessary tools from real geometric algebra are introduced and a real geometric interpretation is given to the eigenvalues and eigenvectors. The latter are seen to be two...