What’s all the fuss about Disney? : narcissistic and nostalgic tendencies in popular Disney storyworlds

This paper seeks to study the narcissistic and nostalgic desires cultivated in cinematic audiences by modern Disney story franchises. Through its storyworlds, the Disney conglomerate is a key player in the cultural formation and consciousness of global audiences, young and old. The research demonstrates how narcissism and nostalgia are used as a means for personal development and amelioration of the present condition as well as a means of control over the viewers’ self-understanding and knowledge of past and present realities. The paper explores Baudrillard’s concept of controlled narcissism which illustrates how a subject’s self-development is hampered by media conglomerates that disseminate a fixed formula which becomes their means of exercising control over time, space and identity formation. This paper also considers the use of nostalgia by media and entertainment industries. Using the works of Fredric Jameson, Linda Hutcheon and Svetlana Boym, this study investigates the commodification of nostalgia which promotes a recyclable and romanticized view of the past as well as the prospective use of nostalgia which allows the viewer to critically reflect on past and present times. These theories are applied to two contemporary case studies to understand better how narcissistic and nostalgic tendencies are manifested in the complex and transformative journeys of the flawed protagonists in contemporary popular Disney storyworlds.peer-reviewe

The complex AGM, periods of elliptic curves over C and complex elliptic logarithms

We give an account of the complex Arithmetic-Geometric Mean (AGM), as first studied by Gauss, together with details of its relationship with the theory of elliptic curves over \C, their period lattices and complex parametrisation. As an application, we present efficient methods for computing bases for the period lattices and elliptic logarithms of points, for arbitrary elliptic curves defined over \C. Earlier authors have only treated the case of elliptic curves defined over the real numbers; here, the multi-valued nature of the complex AGM plays an important role. Our method, which we have implemented in both \Magma\ and \Sage, is illustrated with several examples using elliptic curves defined over number fields with real and complex embeddings.Comment: The addional file elog_ex.sage contains a Sage script for the examples in the last section of the paper, and the file elog_ex.out contains the result of running that script with Sage version 5.

The L-functions and modular forms database project

The Langlands Programme, formulated by Robert Langlands in the 1960s and since much developed and refined, is a web of interrelated theory and conjectures concerning many objects in number theory, their interconnections, and connections to other fields. At the heart of the Langlands Programme is the concept of an L-function. The most famous L-function is the Riemann zeta-function, and as well as being ubiquitous in number theory itself, L-functions have applications in mathematical physics and cryptography. Two of the seven Clay Mathematics Million Dollar Millennium Problems, the Riemann Hypothesis and the Birch and Swinnerton-Dyer Conjecture, deal with their properties. Many different mathematical objects are connected in various ways to L-functions, but the study of those objects is highly specialized, and most mathematicians have only a vague idea of the objects outside their specialty and how everything is related. Helping mathematicians to understand these connections was the motivation for the L-functions and Modular Forms Database (LMFDB) project. Its mission is to chart the landscape of L-functions and modular forms in a systematic, comprehensive and concrete fashion. This involves developing their theory, creating and improving algorithms for computing and classifying them, and hence discovering new properties of these functions, and testing fundamental conjectures. In the lecture I gave a very brief introduction to L-functions for non-experts, and explained and demonstrated how the large collection of data in the LMFDB is organized and displayed, showing the interrelations between linked objects, through our website www.lmfdb.org. I also showed how this has been created by a world-wide open source collaboration, which we hope may become a model for others.Comment: 14 pages with one illustration. Based on a plenary lecture given at FoCM'14, December 2014, Montevideo, Urugua

Landmarks in Maltese Constitutional History 1849-1974

In a few words - alas, too few to do justice to this subject – the author commemorates, as this beautiful medal is also intended to do, an event which is undoubtedly the greatest one in Malta's modern history: the achievement of independence. In doing so, he begs forgiveness if he seems to overindulge in the use of the first person singular. But, to some extent this is unavoidable given that the events running up to Independence he had the good fortune of being right at the forefront and literally in the thick of it all.peer-reviewe

Primary children’s understanding and relationship with cartoon characters : a multimodal praxis-based research experience

This paper presents the research outcomes of a two-year research venture conducted by Attard (2019) which links theory to classroom-based praxis. In brief, the first part of the paper presents a sound theoretical grounding based on international literature about primary school children’s understanding and relationship with cartoon characters. Later, based on the critical theoretical literature review presented in the first part, the paper links the outcomes to two levels of praxis. Initially, it presents how nine / ten-year-old children attending Maltese primary schools understand and relate to cartoon characters based on their everyday cartoon watching experiences. Then, based on an original multimodal framework (Cremona, 2017), as a main conclusion, a set of practical multimodal suggestions are proposed. These suggestions are intended to be used by educators, parents or guardians with primary school children.peer-reviewe

Black Box Galois Representations

We develop methods to study $2$-dimensional $2$-adic Galois representations $\rho$ of the absolute Galois group of a number field $K$, unramified outside a known finite set of primes $S$ of $K$, which are presented as Black Box representations, where we only have access to the characteristic polynomials of Frobenius automorphisms at a finite set of primes. Using suitable finite test sets of primes, depending only on $K$ and $S$, we show how to determine the determinant $\det\rho$, whether or not $\rho$ is residually reducible, and further information about the size of the isogeny graph of $\rho$ whose vertices are homothety classes of stable lattices. The methods are illustrated with examples for $K=\mathbb{Q}$, and for $K$ imaginary quadratic, $\rho$ being the representation attached to a Bianchi modular form. These results form part of the first author's thesis.Comment: 40 pages, 3 figures. Numerous minor revisions following two referees' report

Tetrahedral Elliptic Curves and the local-global principle for Isogenies

We study the failure of a local-global principle for the existence of $l$-isogenies for elliptic curves over number fields $K$. Sutherland has shown that over $\mathbb{Q}$ there is just one failure, which occurs for $l=7$ and a unique $j$-invariant, and has given a classification of such failures when $K$ does not contain the quadratic subfield of the $l$'th cyclotomic field. In this paper we provide a classification of failures for number fields which do contain this quadratic field, and we find a new `exceptional' source of such failures arising from the exceptional subgroups of \mbox{PGL}_2(\mathbb{F}_l). By constructing models of two modular curves, $X_{\text{s}}(5)$ and $X_{S_4}(13)$, we find two new families of elliptic curves for which the principle fails, and we show that, for quadratic fields, there can be no other exceptional failures.Comment: The attachment contains annotated Sage code with details of the computation

A Further Note on a Formal Relationship Between the Arithmetic of Homaloidal Nets and the Dimensions of Transfinite Space-Time

A sequence of integers generated by the number of conjugated pairs of homaloidal nets of plane algebraic curves of even order is found to provide an >exact< integer-valued match for El Naschie's primordial set of fractal dimensions characterizing transfinite heterotic string space-time.Comment: 3 pages, no figures, submitted to Chaos, Solitons & Fractal

Constructing non-trivial elements of the Shafarevich-Tate group of an Abelian Variety over a Number Field

The second part of the Birch and Swinnerton-Dyer (BSD) conjecture gives a conjectural formula for the order of the Shafarevich-Tate group of an elliptic curve in terms of other computable invariants of the curve. Cremona and Mazur initiated a theory that can often be used to verify the BSD conjecture by constructing non-trivial elements of the Shafarevich-Tate group of an elliptic curve by means of the Mordell-Weil group of an ambient curve. In this paper, we generalize Cremona and Mazur's work and give precise conditions under which such a construction can be made for the Shafarevich-Tate group of an abelian variety over a number field. We then give an extension of our general result that provides new theoretical evidence for the BSD conjecture.Comment: 18 page