Juliane Fonseca de Oliveira
University of Porto, Portugal
Juliane Oliveira has completed her B.S. in Mathematics from Federal University of Bahia (UFBA), Brazil, with final work related to studies of Einstein equation on Flag Manifolds. She is currently a PhD student in the Department of Mathematics at University of Porto, working in Bifurcation and Crystallography Theory. In particular, she wants to describe a mathematical tool in order to understand the transition of dimensionality in Reaction Diffusion systems in the Turing instability regime.
In the study of pattern formation in symmetric physical systems a 3-dimensional structure in thin domains is often modelled as 2-dimensional one. As a contrast, in this talk we use the full 3-dimensionality of the problem to give a theoretical interpretation and possibly decide whether the pattern seen in such systems naturally occur in either 2- or 3- dimension. For this purpose, we are concerned with functions in 3-dimention that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. In particular, we introduce a formalism to explain how the study of bifurcation theory, in the context of symmetries, is applied to the theory of projection we present.