Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.

Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory.This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics.

La gestion ambiental de un residuo peligroso comprende diferentes etapas generacion, minimizacion, transporte, valorizacion, tratamiento y disposicion. Este trabajo explora dos tecnologias para el tratamiento y disposicion final de un residuo peligroso, tierra Fuller contaminada con aceite dielectrico: fisico-quimica y biologica. La tecnologia fisico-quimica uso hexano como solvente, y se alcanzaron remociones del aceite dielectrico del 87% en la tierra Fuller contaminada, con una relacion tierra Fuller/solvente de 1:8 p/v, velocidad de agitacion de 100 rpm y un tiempo de contacto de 30 min. La tierra Fuller recuperada registro una densidad aparente de 0.641 gr/ml, una densidad real de 2.231 gr/ml y una porosidad de 72.075 %, lo que indica que dicha tierra esta muy cercana en sus caracteristicas fisicas a la tierra Fuller limpia. Para la tecnologia biologica se trato la tierra contaminada en un biorreactor biologico de tierra activada, evaluando la velocidad de agitacion y el tiempo de degradacion necesario para alcanzar los niveles de descontaminacion que permitan disponer el residuo en un relleno sanitario convencional sin riesgo para la salud humana y de los ecosistemas."