We compute the integral homology (including torsion), the topological K-theory, and the Hodge structure on cohomology of Calabi-Yau threefold hypersurfaces and complete intersections in Gorenstein toric Fano varieties. The methods are purely topological.

Charles F. Doran John W. Morgan

We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.

Brent Doran Jun Yu

We have ported the cmbfast package to the C++ programming language to produce cmbeasy, an object oriented code for the cosmic microwave background. The code is available at www.cmbeasy.org. We sketch the design of the new code, emphasizing the benefits of object orientation in cosmology, which allow for simple substitution of different cosmological models and gauges. Both gauge invariant perturbations and quintessence support has been added to the code. For ease of use, as well as for instruction, a graphical user interface is available.

Michael Doran

We investigate a link between the running of the fine structure constant $\alpha$ and a time evolving scalar dark energy field. Employing a versatile parameterization for the equation of state, we exhaustively cover the space of dark energy models. Under the assumption that the change in $\alpha$ is to first order given by the evolution of the Quintessence field, we show that current Oklo, Quasi Stellar Objects and Equivalence Principle observations restrict the model parameters considerably stronger than observations of the Cosmic Microwave Background, Large Scale Structure and Supernovae Ia combined.

Michael Doran

We show that collider experiments have the potential to exclude a light scalar field as well as generic models of modified gravity as dark energy candidates. Our mechanism uses the spectrum radiated by black holes and can equally well be applied to determine the number of light degrees of freedom. We obtain the grey body factors for massive scalar particles and calculate the total emissivity. While the Large Hadron Collider (LHC) may not get to the desired accuracy, the measurement is within reach of next generation colliders.

Michael Doran Joerg Jaeckel

We constrain the evolution of the dark energy density from Cosmic Microwave Background, Large Scale Structure and Supernovae Ia measurements. While Supernovae Ia are most sensitive to the equation of state $w_0$ of dark energy today, the Cosmic Microwave Background and Large Scale Structure data best constrains the dark energy evolution at earlier times. For the parametrization used in our models, we find $w_0 < -0.8$ and the dark energy fraction at very high redshift $\Omega_{early} < 0.03$ at 95 per cent confidence level.

Michael Doran Khamphee Karwan Christof Wetterich

We take a null hypersurface (the causal horizon) generated by a congruence of null geodesics as the boundary of the Doran-Lobo-Crawford spacetime, to be the place where the Brown-York quasilocal energy is located. The components of the outer and inner stress tensors are computed and shown to depend on time and on the impact parameter $b$ of the test particle trajectory. The surface energy density $\sigma$ on the boundary is given by the same expression as that obtained previously for the energy stored on a Rindler horizon.

Hristu Culetu

Motivated by a conjecture of Lian and Yau concerning the mirror map in string theory, we determine when the mirror map q-series of certain elliptic curve and K3 surface families are Hauptmoduln (genus zero modular functions). Our geometric criterion for modularity characterizes orbifold uniformization properties of their Picard-Fuchs equations, effectively demystifying the mirror-moonshine phenomenon. A longer, more comprehensive treatment of these results will appear shortly.

Charles F. Doran

We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P^2, induced from those for seven points on P^1. The seven point ball quotient example DM(2^5,1^2) does not appear on Mostow's original list, but does appear on Thurston's corrected version. We show that DM(2^5,1^2) is a finite cover of the moduli space of cubic surfaces M_C endowed with the ball quotient structure G_C\B^4 of Allcock, Carlson, and Toledo. This answers a question of Allcock about the commensurability of G_C with the monodromy groups of Deligne-Mostow hypergeometric functions.

Brent R. Doran

This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the Dirac equation, operators and monogenics, the Hydrogen atom, propagators and scattering theory, spin precession, tunnelling times, spin measurement, multiparticle quantum mechanics, relativistic multiparticle wave equations, and semiclassical mechanics.

C. J. L. Doran A. N. Lasenby S. F. Gull S. Somaroo A. D. Challinor