The Exact Sciences

Three periods may be distinguished in the development of scientific research and teaching in France during the twentieth century: the years prior to 1914; the interwar period; and the balance of the century, from 1945. Despite the very different circumstances that prevailed during these periods, a certain structural continuity has persisted until the present day and given the development of the exact sciences in France its distinctive character

A History of Complex Simple Lie Algebras

In 1869, prompted by his work in differential equations, Sophus Lie wondered about categorizing what he called “closed systems of commutative transformations,” while around the same time, Wilhelm Killing’s work on non-Euclidean geometry encountered related topics. As mathematicians recognized this as a division of abstract algebra, the area became known as “continuous transformation groups, but we now refer to them as Lie groups. Patterns and structures emerged from their work, such as describing Lie groups in connection with their associated Lie algebras, which can be categorized in many important ways. In this paper, we focus on Lie algebras over the complex numbers, and how simplicity and the related notion of semisimplicity, as well as root spaces and their representations, reveal that there are, up to isomorphism, surprisingly few simple complex Lie algebras, a result which Killing examined intuitively. Élie Cartan’s influence on the development of the theory of Lie algebras, though chronologically slightly later, was key to making the theory of Lie algebras the influential topic it continues to be today. He brought the rigor Lie preferred to bear on ideas and patterns generated by Killing; among other impacts of his approach, in solving the classification problem of simple complex Lie algebras

Professor LLUÍS SANTALÓ (1911-2001)

On 22 November, aged 90, the great mathematician Lluís Antoni Santaló i Sors died in Argentina. He was an outstanding exponent of Integral Geometry, a great teacher and disseminator of scientific understanding, and a person of great human value. He had over 250 publications to his name, among which are books which have had considerable influence on our mathematic community, such as his Geometría Proyectiva. These lines are intended as an early sketch which can serve as the basis for the much fuller homages he deserves

Black Holes in Supergravity with Applications to String Theory

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 17-06-201