Inflation and Eternal Inflation

The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Vilenkin's proposal for avoiding these problems is also discussed.Comment: 27 pages, including 5 figures, LaTeX (elsart macros for Physics Reports, included). To be published in the David Schramm Memorial Volume of Physics Report

Volumes of balls in Riemannian manifolds and Uryson width

If $(M^n, g)$ is a closed Riemannian manifold where every unit ball has volume at most $\epsilon_n$ (a sufficiently small constant), then the $(n-1)$-dimensional Uryson width of $(M^n, g)$ is at most 1.Comment: 26 page

The Local and the Global: Hokusai's Great Wave in Contemporary Product Design

This article examines the impact and significance of Hokusai’s so-called The Great Wave in contemporary product promotion and design. Arguably Japan’s first global brand, this influential 19th-century woodcut has been widely adopted to style and advertise a wide range of merchandise, most of it neither manufactured in Japan nor primarily dependent on the commodification of the Japanese aesthetic or locale. Interpretation of the varied contexts in which the distinctive cresting wave appears challenges essentialising narratives that see the modern adoption of such traditional non-Western motifs as expressions of Japonisme or Orientalism. Taking an interdisciplinary approach that brings to bear design and global studies theory, Guth instead focuses on how this highly adaptive motif, with its connotations of being both nowhere and everywhere, serves to mediate between the local and the global. Despite the ubiquity of The Great Wave in the commercial realm, to date there have been no studies of its cross-cultural significance. To carry out this project, Guth conducted extensive research into the merchandise on offer in museum shops and online websites, and among global brands such as Patagonia that have made use of the motif. Guth also interviewed designers and users of the products to assess the rationale for the choice of this form of branding and the degree to which awareness of its origins influenced purchases. Guth was invited to present this new research on the global commercial impact of Hokusai’s The Great Wave at an international conference on ‘Hokusai in Context’ in Berlin in 2011. The conference paper and resulting published essay were developed to form a chapter in a book-length investigation into the global iconicity of Hokusai’s wave from its creation to the present day. The book, Hokusai’s Great Wave: Biography of a global icon, will be published by University of Hawai’i Press in 2014

A short proof of the multilinear Kakeya inequality

We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.Comment: 7 pages, minor revision, accepted for publication in the Mathematical Proceedings of the Cambridge Philosophical Societ