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The goal of these lectures is to define mathematical gauge theory and relate it to gauge theory (from physics).

This is an introductory course presenting the basics of the AdS/CFT duality. On the way, it will present some interesting physical concepts which are worth being acquainted wth,  independently of anti-de Sitter or string theory, such as for example aspects of: confromal filed theories in d>2, the renormalization group, non-abelian gauge theories,  the large-N limit, black hole thermodynamics, semiclassical gravity. 

These lectures present the study of instabilities or bifurcations of nonlinear systems and the resulting dynamic behaviors.

Quantum information combines quantum physics and information theory, leading to a conceptual shift in both disciplines. By implementing quantum protocols in physical systems and reformulating quantum physics in terms of information and logical operations, we gain powerful tools to investigate the distinctive features of quantum mechanics - such as its divergence from classical physics and the nature of the quantum-to-classical transition.

The aim of the course is to present some advanced theoretical tools in quantum mechanics with an emphasis on open-system dynamics, scattering theory and many-body physics.