This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and a proof that this leads in a simple manner to the known Schwinger terms (Mickels...

In particular, the Julia set of z + c1 is locally connected if c1 ∈ [−2, 1/4] and totally disconnected if c1 ∈ R \ [−2, 1/4] (note that [−2, 1/4] is equal to the set of parameters c1 ∈ R for which the critical point c = 0 does not escape to infinity). This answers a question posed by Milnor, see [Mil1]. We should emphasize that if the ω-limit set ω(c) of the critical point c = 0 is not minimal ...

A WKB method was recently used to extend rapid distortion theory (RDT) to initially inhomogeneous turbulence strained by irrotational mean flows [S.V. Nazarenko, N. Kevlahan, B. Dubrulle, J. Fluid Mech. 390 (1999) 325]. This theory takes into account the feedback of turbulence on the mean flow, and it was used by Nazarenko et al. to explain the effect of strain reduction caused by turbulence ob...

Hubbard trees are invariant trees connecting the points of the critical orbits of postcritically finite polynomials. Douady and Hubbard [DH1] introduced these trees and showed that they encode the essential information of Julia sets in a combinatorial way. The itinerary of the critical orbit within the Hubbard tree is encoded by a (pre)periodic sequence on {0, 1} called kneading sequence. We pr...

Fishes are known to have a great deal of variability in their vertebrae especially near the occipital region. Despite this observed variability, there is new and compelling evidence for developmental conservatism in the region for actinopterygians (Bemis & Forey 2001; Britz & Johnson 2010; Johnson & Britz 2010). Authors have even hypothesized that the occiput could be homologous among chondrich...

GPAT (EC 2.3.1.15) catalyzes the first step in phospholipid and triglyceride synthesis. In the former context, it is implicated in chilling resistance in plants, through its role in selecting the fatty acids that are incorporated into chloroplast lipids and then into membranes. The GPAT from chillingresistant plants such as pea is highly selective for oleic acid, whereas the enzyme from chillin...

In this paper, we discuss several aspects of Julia sets, as well as those of the Mandelbrot set. We are interested in topological properties such as connectivity and local connectivity, geometric properties such as Hausdorff dimension and Lebesgue measure, and complex analytic properties such as holomorphic removability. As one can easily see from the pictures of numerical experiments, there is...

We describe an interesting interplay between symbolic dynamics, the structure of the Mandelbrot set, permutations of periodic points achieved by analytic continuation, and Galois groups of certain polynomials. In the early 1990’s, Devaney asked the question: how can you tell where in the Mandelbrot set a given external ray lands, without having Adrien Douady at your side? We provide an answer t...