19. Mikko Lavinto, Syksy Rasanen, Sebastian J. Szybka Average expansion rate and light propagation in a cosmological Tardis spacetime JCAP, vol. 12, p. 051 (2013). [abstract] [preprint] [journal] [download] 
Abstract: We construct the first exact statistically homogeneous and isotropic cosmological solution in which inhomogeneity has a significant effect on the expansion rate. The universe is modelled as a Swiss Cheese, with Einsteinde Sitter background and inhomogeneous holes. We show that if the holes are described by the quasispherical Szekeres solution, their average expansion rate is close to the background under certain rather general conditions. We specialise to spherically symmetric holes and violate one of these conditions. As a result, the average expansion rate at late times grows relative to the background, i.e. backreaction is significant. The holes fit smoothly into the background, but are larger on the inside than a corresponding background domain: we call them Tardis regions. We study light propagation, find the effective equations of state and consider the relation of the spatially averaged expansion rate to the redshift and the angular diameter distance. 
20. Nicolas Franco, Michał Eckstein An algebraic formulation of causality for noncommutative geometry Class. Quantum Grav., vol. 30, p. 135007 (2013). [abstract] [preprint] [journal] 
Abstract: We propose an algebraic formulation of the notion of causality for spectral triples corresponding to globally hyperbolic manifolds with a well defined noncommutative generalization. The causality is given by a specific cone of Hermitian elements respecting an algebraic condition based on the Dirac operator and a fundamental symmetry. We prove that in the commutative case the usual notion of causality is recovered. We show that, when the dimension of the manifold is even, the result can be extended in order to have an algebraic constraint suitable for a Lorentzian distance formula. 
21. Christa R. Ölz, Sebastian J. Szybka Conformal and projection diagrams in LaTeX (2013). [abstract] [preprint] 
Abstract: In general relativity, the causal structure of spacetime may sometimes be depicted by conformal CarterPenrose diagrams or a recent extension of these  the projection diagrams. The introduction of conformal diagrams in the sixties was one of the progenitors of the golden age of relativity. They are the key ingredient of many scientific papers. Unfortunately, drawing them in the form suitable for LaTeX documents is timeconsuming and not easy. We present below a library that allows one to draw an arbitrary conformal diagram in a few simple steps. 
22. A. Gierzkiewicz, K. Wójcik Lefschetz sequences and detecting of periodic points Discrete and Continuous Dynamical Systems  Series A, vol. 32, pp. 81100 (2012).

Abstract: Abstract 
23. Andrzej Sitarz On the geometry of kappadeformation International Journal of Geometric Methods in Modern Physics, vol. 9, pp. 12610111261021 (2012). [abstract] [journal] [download] 
Abstract: We present a brief outline of recent and new results on the mathematical structure underlying the kappadeformed space. We suggest to turn attention to the observable C*algebra of kappadeformed coordinates and its Galilean symmetries.
*supported by the grant from The John Templeton Foundation 
24. Heller, Michael; Pysiak, Leszek; Sasin, Wiesław Quantum effects in a noncommutative Friedman world model Canadian Journal of Physics, vol. 90, pp. 223228 (2012). [abstract] [journal] [download] 
Abstract: We present a noncommutative version of the closed Friedman world model and show how its classical space–time geometry can be expressed in terms of typically quantum mathematical structures, namely in terms of an operator algebra on a family of Hilbert spaces. The operator algebra can be completed to the von Neumann algebra , but the geometry cannot be prolonged from to . This mathematical fact is a stumbling block in creating full quantum gravity theory. Two effects appearing in this model, generation of matter and probabilistic properties of singularities, are also discussed.
*supported by the grant from The John Templeton Foundation 