This course is an introduction to geometrical critical phenomena and their description by means of algebraic, probabilistic and quantum field theoretical techniques. 

This is the follow-up couse to the quantum field theory class of the first semester. Topics we will cover include non-abelian gauge symmetry, spontaneous symmetry breaking, and the Higgs mechanism, all needed to understand the inner workings of the Standard Model, which we shall discuss in some detail.

The aim of this course is to introduce the most important topics needed to understand how we can test the Standard Model, then why and how we must go beyond it. It is aimed not just at future practitioners, but at anyone wanting to study High Energy 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. 

A Dark Matter Journey from Particle Physics to Modern Cosmology.

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

The theory of groups and their representations is a central topic which studies symmetries in various contexts occurring in pure or applied mathematics as well as in other sciences, most notably in physics.