Felix Wierstra: Deformation Quantization

In this talk I will give an introduction to deformation quantization. In physics there are two theories, classical mechanics which describes systems that are big compared to Planck's constant and quantum mechanics which describes small systems. One of the key differences between these two theories is that in classical mechanics the algebra of observables is commutative and in quantum mechanics the algebra of observables is non commutative. The idea of deformation quantization is then to describe the the algebra of observables in quantum mechanics as a small deformation of the algebra of classical observables. This if we take the limit in which Planck's constant goes to zero we end up with classical mechanics.  In this talk I will explain what this means and give a brief sketch of Kontsevich's proof that this is always possible. Almost no knowledge of physics is required as background.