General Relativity is a very successful theory that has not yet been exhaustively tested in the strong field regime. Black holes are simple objects predicted in the theory and are a good arena to study some strong field features of General Relativity. With a simple idea we have been able to construct (analytically) an event horizon that describes the merger of two black holes, one of them being much more massive than the other one.

Presentaré una panorámica de algunas ideas básicas que se usan en el estudio de los invariantes adiabáticos de sistemas Hamiltonianos, junto con algunos resultados recientes obtenidos conjuntamente con Yury Vorobiev y Misael Avendaño (de la Unison), que esperamos se puedan extender al caso cuántico.

La noción de cuantización surgió en la física como una herramienta para describir el universo a escalas microscópicas. Con el paso de tiempo, los problemas y retos a los que ha llevado su entendimiento han dado lugar a ejemplos y construcciones de poderosos invariantes en la geometría y topología de variedades de dimensiones pequeñas. En esta charla me concentraré en describir como el problema de cuantización geométrica en la teoría de Chern-Simons conlleva a la construcción de representaciones de grupos modulares de Teichmüller para superficies de Riemann, elaborando sobre el origen de dicha construcción en el trabajo de Atiyah, así como algunas de sus consecuencias y ramificaciones.

Observable currents are spacetime local objects that induce physical observables when integrated on an auxiliary codimension one surface. Since the resulting observables are independent of local deformations of the integration surface, the currents themselves carry most of the information about the induced physical observables.

I study observable currents in a multisymplectic framework for lagrangian field theory over discrete spacetime and prove that the observables induced by them separate points in the space of solutions. A Poisson bracket gives the space of observable currents the structure of a Lie algebra. Peierls bracket for bulk observables gives a map between equivalence classes of bulk observables and observable currents. The study covers scalar fields, nonlinear sigma models and gauge theories (including gauge theory formulations of general relativity) on the lattice.

A talk on the same subject was given in IFM two months ago. In this occasion the objective of the exposition will be to introduce the subject starting from the most basic assumptions, with the intention that every participant to understand the details of the proposal and to participate in crafting the aspects that are still immature.