An Introduction to Riemann-Cartan Geometry and Gravity.

These lectures introduce some mathematical techniques to study Riemann-Cartan geometries, and we show how to apply them in the context of gravity. In particular, we illustrate how differential forms and connections on fiber bundles are valuable tools for constructing action principles for gravity and studying its dynamics and wave operator behavior. Furthermore, these tools prove helpful for analyzing some torsional effects on cosmological evolution and propagation of gravitational waves, which future observations may measure.

Two lectures on Holographic duality

We will introduce AdS/CFT correspondence between anti-de Sitter (AdS) gravity in d+1 dimensions and Conformal Field Theory (CFT) in d dimensions. We shall analyse matching of physical observables and symmetries between these two theories, and discuss appearance of holographic anomalies in an even-dimensional CFT.

As an application, we will focus on a quantum field theory at the finite temperature. We shall argue that this theory is holographically dual to a black hole in AdS gravity with the same Hawking temperature. We will apply a holographic prescription to build a holographic superconductor and explore its physical properties.

First order formalism & Chern-Simons gravity