# IST Lecture Series in Algebraic Geometry & Physics

### Microlocal analysis, quantization and integrable systems (I)

In the first lecture, I will present the general problem of quantization. Starting from a classical phase space (symplectic manifold), how to define a quantum space (Hilbert space) and transform Hamiltonians into linear operators? I will give details about the left, right, and Weyl quantization on ${\mathbb R}^{2n}$.