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In the first part of this paper we outline the constructions and propertiesof Fedosov star product and Berezin-Toeplitz star product. In the second partwe outline the basic ideas and recent developments on Yau-Tian-Donaldsonconjecture on the existence of K\"ahler metrics of constant scalar curvature.In the third part of the paper we outline recent results of both authors, andin particular show that the constant scalar curvature K\"ahler metric problemand the study of deformation quantization meet at the notion of trace (density)for star product. We formulate a cohomology formula for the invariant ofK-stability condition on K\"ahler metrics with constant Cahen-Gutt momentum.

Deformation quantization and K\"ahler geometry with moment map