Markov chains, R\mathscr R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via M\"obius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth birthday; 71 pages; final version to appear in IJA

Phenomenology of Visual Arts in William Faulkner\u27s the Sound and the Fury and as I Lay Dying

The early decades of the 20th century marked drastic changes in philosophy, science, visual arts, literature, and music. In philosophy, this change occurred in the work of Edmund Husserl whose Phenomenology introduced a new “way of knowing” or epistemology. In art, the exhibition of Pablo Picasso’s Cubist Les Demoiselles d’Avignon (1907), given its rebellious nature, began an innovative artistic tradition which called for a new “way of seeing.” Phenomenology as theory and Cubism as practice shared a common aim: to re-vision the world—an aim of many Modernist movements. Modernism is an umbrella term for a mélange of artistic schools and styles, which are characterized by such features as aesthetic self-consciousness, structural and thematic fragmentation, and a complexity of representation. Modernism contains Phenomenology and Cubism as twin attempts to re-vision and reconstruct the viewer’s experience of the object-world. The aim of this thesis is twofold: 1) to outline the complex vocabulary of Husserlian Phenomenology and Cubism, and 2) to apply those vocabularies to William Faulkner’s texts. As examples of visual and phenomenological perspectivism, Faulkner’s The Sound and The Fury and As I Lay Dying were explored for their correlations to Husserlian Phenomenology and Cubism. By utilizing artistic techniques drawn from Fauvism, Surrealism, and, Cubism, Faulkner’s novels provide literary samples for how artists reconstruct the world visually through their art. Husserlian Phenomenology likewise aims to reconstruct our human perceptions and experience

Revisiting the past; archive, memory and the passage of time in the installation artworks

MT 201

Renaissance Fun: The machines behind the scenes

Renaissance Fun is about the technology of Renaissance entertainments in stage machinery and theatrical special effects; in gardens and fountains; and in the automata and self-playing musical instruments that were installed in garden grottoes. How did the machines behind these shows work? How exactly were chariots filled with singers let down onto the stage? How were flaming dragons made to fly across the sky? How were seas created on stage? How did mechanical birds imitate real birdsong? What was ‘artificial music’, three centuries before Edison and the phonograph? How could pipe organs be driven and made to play themselves by waterpower alone? And who were the architects, engineers, and craftsmen who created these wonders? All these questions are answered. At the end of the book we visit the lost ‘garden of marvels’ at Pratolino with its many grottoes, automata and water jokes; and we attend the performance of Mercury and Mars in Parma in 1628, with its spectacular stage effects and its music by Claudio Monteverdi – one of the places where opera was born. Renaissance Fun is offered as an entertainment in itself. But behind the show is a more serious scholarly argument, centred on the enormous influence of two ancient writers on these subjects, Vitruvius and Hero. Vitruvius’s Ten Books on Architecture were widely studied by Renaissance theatre designers. Hero of Alexandria wrote the Pneumatics, a collection of designs for surprising and entertaining devices that were the models for sixteenth and seventeenth century automata. A second book by Hero On Automata-Making – much less well known, then and now – describes two miniature theatres that presented plays without human intervention. One of these, it is argued, provided the model for the type of proscenium theatre introduced from the mid-sixteenth century, the generic design which is still built today. As the influence of Vitruvius waned, the influence of Hero grew