A level raising result for modular Galois representations modulo prime powers

In this work we provide a level raising theorem for $\mod \lambda^n$ modular Galois representations. It allows one to see such a Galois representation that is modular of level $N$, weight 2 and trivial Nebentypus as one that is modular of level $Np$, for a prime $p$ coprime to $N$, when a certain local condition at $p$ is satisfied. It is a generalization of a result of Ribet concerning $\mod \ell$ Galois representations.Comment: 5 page

Classification of engineered topological superconductors

I perform a complete classification of 2d, quasi-1d and 1d topological superconductors which originate from the suitable combination of inhomogeneous Rashba spin-orbit coupling, magnetism and superconductivity. My analysis reveals alternative types of topological superconducting platforms for which Majorana fermions are accessible. Specifically, I observe that for quasi-1d systems with Rashba spin-orbit coupling and time-reversal violating superconductivity, as for instance due to a finite Josephson current flow, Majorana fermions can emerge even in the absence of magnetism. Furthermore, for the classification I also consider situations where additional "hidden" symmetries emerge, with a significant impact on the topological properties of the system. The latter, generally originate from a combination of space group and complex conjugation operations that separately do not leave the Hamiltonian invariant. Finally, I suggest alternative directions in topological quantum computing for systems with additional unitary symmetries.Comment: To appear in New Journal of Physics for the Focus on Majorana Fermions in Condensed Matter; Final version 19 pages, 6 figures: a new section was added concerning the appearance of MFs in two coupled Rasba semiconducting wires with proximity induced superconductivity and a finite supercurrent flow, without the application of a magnetic field. Generally improved discussion and references adde

A Compositional Model for the Formal Specification of User Interface Software

Submitted for the degree of Doctor of Philosoph

John Tzetzes and the blemish examiners : a Byzantine teacher on schedography, everyday language and writerly disposition

The paper focuses on John Tzetzes (ca. 1110-after 1166), a well-known teacher and scholar of the Komnenian era, with the aim of examining two issues. On the one hand, Tzetzes’ opinions about the teaching practice of schedography are collected and analysed, while, on the other, his opinions about everyday language and its possible uses are scrutinised through a close reading of many different passages from his works. In particular, the long epilogue of his Theogony (with its three parts united for the first time on the printed page), written for the sebastokratorissa Eirene around the middle of the Twelfth Century, is discussed in detail as a unique source of debate on what is the appropriate way of addressing and writing for audiences of different social and educational status. The analysis and interpretation of the texts demonstrates that the “idiosyncratic” personality Tzetzes shows in his writings is not a purely personal matter, but is strongly related to the competitive environment of the capital and to Tzetzes’ “middle-class” position in the Constantinopolitan society. The paper also demonstrates that the boundaries of usage between “learned” and “colloquial” discourse are quite fluid and this fluidity can be used in certain contexts to the advantage of a teacher in promoting his status and financial success, or to his disadvantage if he has to defend his choices against a rival. The paper ends with a broader analysis of the term oijkonomiva used by Tzetzes in the Theogony epilogue and of the meaning of this term within the system of literary patronage under the Komnenoi