Hyperbolic Geometry

Exercises, exam questions and solutions for a fourth year hyperbolic geometry course. Diagrams for the questions are all together in the support.zip file, as .eps files

Large Scale Structure of Metric Spaces

How the mathematical concept of Coarse Geometries is useful to analysing the Web

The cultural magazines as spaces of resistence in the lasta argentinian militar dictatorship. From the “El Expreso Imaginario” to “El Porteño”, 1976 – 1983

Although they were a few, there were places during the military dictatorship, which produced innovative cultural goods, in continuity with experiences of the artistic avant-garde in the sixties. Alongside the political and military repression  they could articulate in their environment groups identified with alternative aesthetic  codes, in opposition to the dominant culture in the period. The first one of the aces  we examine in the article, El Expreso Imaginario is a privileged place where we may regard the origins of the traits of that social space. Towards the end of  the dictatorship, another one like El Porteño, marks a new era, even if we can  establish various continuities with the first one. The circulation places of these ideas and practices were often taking place in cellars and other hiding places. Is  that because they take the literal sense of underground in the eighties to groups  who having been part of that story or not, were willing to receive his inspiring legacy. Between both magazines we   fer identifies the transition from one state of the field to another, identifying the evolution of these zone of the culture field.

Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Delineating difference and spaces of resistance : reading the Nana’s Silence in Rosario Castellanos’ ''Balún Canán''

A escritora mexicana Rosario Castellanos incorpora silêncios em suas obras de uma forma que permite ao leitor a questionar o próprio significado da agência e da natureza da subjetividade de uma protagonista feminina. Silêncios tendem a criar brechas no texto, iluminando as diferenças sociais e raciais que a narração em primeira pessoa foge. Além disso, é revelado que o sujeito se imagina em oposição ao silêncio de mulheres menos privilegiadas, e que realmente não existe um local em que o subalterno pode falar. Este projecto se centra em seu romance Balún Canan (1957), em que a babá Indígena de uma menina complica o desejo de ascender dentro da estrutura patriarcal da sua família mais privilegiada, como a menina descobre que o que faria sua vida confortável é a causa da subjugação de sua “outra mãe.” O texto é desenvolvido em torno de um desejo de falar a partir das margens, e há um esforço claro para dar voz aos subalternos. No entanto, a relação entre a menina e sua babá não é nem romântica nem idealizada; a presença da mulher colonizada resiste a marginalização e ressalta que está sendo coberto no processo de desenvolvimento individual. Ansiedadesurge dentro da narração da menina como ela percebe seu privilégio como membro da classe latifundiária, e a escrita navega entre diferentes manifestações de silêncio: o silenciamento da babá em uma replicação de violência colonial, e a manutenção do silêncio como uma barreira respeitosa.

Dunford-Pettis properties, Hilbert spaces and projective tensor products

We study complete continuity properties of operators onto ℓ2 and prove several results in the Dunford–Pettis theory of JB∗-triples and their projective tensor products, culminating in characterisations of the alternative Dunford–Pettis property for where E and F are JB∗-triples.

Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.