The Algebra & Geometry of Modern Physics

The main theme we are going to focus on in this semester are spinors and their appearance and role in mathematics and physics. Spinors are associated with subspaces in quadratic spaces and can be studied (mathematically) from representation theoretic or geometric perspective. The former one has to do with Clifford algebras and their representations, Spin groups, etc.; the latter approach focuses on the behaviour of spinors under the action of Lie groups. Spinors are also abundant in physics: they are used for the modelling of Fermi fields, the spin-statistics theorem is one of the pillars of quantum field theory, they are intimately related to supersymmetry. Apart from the analysis of spinors, in this semester we will also hear several talks by excellent guests on related (or unrelated) topics.