Statistical Stability for Multi-Substitution Tiling Spaces

Given a finite set ${S_1...,S_k}$ of substitution maps acting on a certain finite number (up to translations) of tiles in \rd, we consider the multi-substitution tiling space associated to each sequence $\bar a\in {1,...,k}^{\mathbb{N}}$. The action by translations on such spaces gives rise to uniquely ergodic dynamical systems. In this paper we investigate the rate of convergence for ergodic limits of patches frequencies and prove that these limits vary continuously with $\bar a$.Comment: 16 pages, 2 figure

Diagrams and harmonic maps, revisited

We extend many known results for harmonic maps from the 2-sphere into a Grassmannian to harmonic maps of finite uniton number from an arbitrary Riemann surface. Our method relies on a new theory of nilpotent cycles arising from the diagrams of F.E. Burstall and the second author associated to such harmonic maps; these properties arise from a criterion for finiteness of the uniton number found recently by the authors with A. Aleman. Applications include a new classification result on minimal surfaces of constant curvature and a constancy result for finite type harmonic maps.Comment: Abstract clarified and minor corrections made to tex

The Museum of the Void

Reflexão sobre as possbilidades de significação e intervenção sobre os enormes espaços vazios gerados pela desactivção de sistemas de silagem de cereais. O potencial programático que o próprio espaço vazio pode, em si, encerrar, é ponto de partida para considerações arquitectónicas, onde se convoca também o valor da proposta projectual como instrumento de ensaio.Trata-se de um texto que integra o catálogo da Exposição homónima, a partir de exploração projectual em domínio académico avançado (Mestrado Integrado)