Abstract: The Spectral Action principle of Noncommutative Geometry has been extremely successful to understand the mathematical structure of the Standard Model of particle physics. However, as a classical framework, it does not yet encompass the corrections of renormalization, which are crucial to understand the quantized version of any field theory. In this talk, I will describe a first attempt to describe renormalization directly within the setting of Noncommutative Geometry, in the case of Yukawa interactions. In particular, I will show that Wetterich's theory of functional renormalization, when applied to a matrix model inspired from the Dirac operator of the Noncommutative Standard Model, reduces to the usual Feynman diagram approach.

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