Geometry and the Mathematical Theory of Quantisation

Geometry is one of the basic pillars of mathematics. At the DMATH we study different directions of modern geometry. A selection of topics under considerations is given by the following list (more can be found at the different teams): algebraic geometry, complex manifolds, differential geometry, symplectic geometry, non-commutative geometry, moduli space problems, higher structures in geometry, algebraic topology, algebraic aspects in geometry, supergeometry, infinite-dimensional Lie algebras, conformal field theory, algebraic aspects of quantum field theory.

Geometry helps us to study and to understand physical reality beyond the naive picture we have from it. Furthermore, geometric techniques and intuitions are used in quite a number of other mathematical and non-mathematical fields which sometimes are very far away from direct perception. A prominent example is the study of the set of solutions of a system of linear or non-linear equations.
We also take up the challenge for mathematicians coming from the theory of quantization and other models of theoretical and mathematical physics. Quantization lies at the basis of all modern theories in physics. It is far away from being  understood as it its nature is rather counter-intuitive. Only mathematics can be of help there.

Authors: Wolf Barth, Oliver Labs - Licence: CC BY-NC-SA