Quantization of spectral curves and DQ-modules

In this talk, I will explain how the quantization of spectral curves associated to Higgs bundles can be studied from the standpoint of DQ-modules. These are objects arising from the study of deformation quantization of complex Poisson manifolds. In particular, I will prove that, given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, there exists an holonomic DQ-module supported by the spectral curve associated to this bundle.