Minimal kernels of Dirac operators along maps

Let $M$ be a closed spin manifold and let $N$ be a closed manifold. For maps $f\colon M\to N$ and Riemannian metrics $g$ on $M$ and $h$ on $N$, we consider the Dirac operator $D^f_{g,h}$ of the twisted Dirac bundle $\Sigma M\otimes_{\mathbb{R}} f^*TN$. To this Dirac operator one can associate an index in $KO^{-dim(M)}(pt)$. If $M$ is $2$-dimensional, one gets a lower bound for the dimension of the kernel of $D^f_{g,h}$ out of this index. We investigate the question whether this lower bound is obtained for generic tupels $(f,g,h)$

On the Expansions in Spin Foam Cosmology

We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expansion. We show that the factorisation of the amplitude originally considered is best interpreted in topological terms. We then consider the next higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector, and conclude that it is necessary to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio

On globally non-trivial almost-commutative manifolds

Within the framework of Connes' noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a 'principal module', which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of 'gauge modules', and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.Comment: 34 pages, minor revision

Potentially Massive and Global Non-Pyrogenic Production of Condensed Black Carbon through Biomass Oxidation

With the increased occurrences of wildfires worldwide, there has been an increase in scientific interest surrounding the chemistry of fire-derived black carbon (BC). Traditionally, wildfire research has assumed that condensed aromatic carbon (ConAC) is exclusively produced via combustion, and thus, ConAC is equated to BC. However, the lack of correlations between ConAC in soils or rivers and wildfire history suggests that ConAC may be produced non-pyrogenically. Here, we show quantitative evidence that this occurs during the oxidation of biomass with environmentally ubiquitous hydroxyl radicals. Pine wood boards exposed to iron nails and natural weather conditions for 12 years yielded a charcoal-like ConAC-rich material. ConAC was also produced during laboratory oxidations of pine, maple, and brown-rotted oak woods, as well as algae, corn root, and tree bark. Back-of-the-envelope calculations suggest that biomass oxidation could be producing massive non-pyrogenic ConAC fluxes to terrestrial and aquatic environments. These estimates (e.g., 163-182 Tg-ConAC/year to soils) are much higher than the estimated pyrogenic BC fluxes (e.g., 128 Tg-ConAC/year to soils) implying that environmental ConAC is primarily non-pyrogenic. This novel perspective suggests that wildfire research trajectories should shift to assessing non-pyrogenic ConAC sources and fluxes, developing new methods for quantifying true BC, and establishing a new view of ConAC as an intermediate species in the biogeochemical processing of biomass during soil humification, aquatic photochemistry, microbial degradation, or mineral-organic matter interactions. We also advise against using BC or pyrogenic carbon (pyC) terminologies for ConAC measured in environmental matrices, unless a pyrogenic source can be confidently assigned

Letter from Frances B. Hatcher, as well as letters of recommendation from Luther M. Defoe, A. Ross Hill, J. C. Jones, and Sam Frank Taylor

Letter concerning a position in the mathematics department at Utah Agricultural College, as well as recommendations

Homotopy types of stabilizers and orbits of Morse functions on surfaces

Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot f\mapsto f \circ h^{-1}$, where $h\in Diff(M)$ and $f \in C^{\infty}(M,P)$. Let $f:M \to P$ be a Morse function and $O(f)$ be the orbit of $f$ under this action. We prove that $\pi_k O(f)=\pi_k M$ for $k\geq 3$, and $\pi_2 O(f)=0$ except for few cases. In particular, $O(f)$ is aspherical, provided so is $M$. Moreover, $\pi_1 O(f)$ is an extension of a finitely generated free abelian group with a (finite) subgroup of the group of automorphisms of the Reeb graph of $f$. We also give a complete proof of the fact that the orbit $O(f)$ is tame Frechet submanifold of $C^{\infty}(M,P)$ of finite codimension, and that the projection $Diff(M) \to O(f)$ is a principal locally trivial $S(f)$-fibration.Comment: 49 pages, 8 figures. This version includes the proof of the fact that the orbits of a finite codimension of tame action of tame Lie group on tame Frechet manifold is a tame Frechet manifold itsel

The Legacy of ERA, Privatization and the Policy Ratchet

This article explores the ways in which the neo-liberal impetus toward the privatization of state schooling signalled in the Education Reform Act 1988 (ERA) has become embedded in the English school system. Four main points are made. First, that ERA itself was of huge strategic rather than substantive importance as far as privatization is concerned. Second, by tracing the lineage of privatization from ERA onwards a 'ratchet' effect of small and incremental policy moves can be identified, which have disseminated, embedded and naturalized privatization within public sector provision. Third, that while privatization has been taken up and taken much further by New Labour than it had been by the Conservatives there are differences between the two sets of governments in the role of privatization in education policy and the role of the state. Fourth, the participation of private providers in the planning and delivery of state services has put the private sector at the very heart of policy. At points the article draws upon interviews conducted with private sector providers. © 2008 Sage Publications