Recently, there have been some very impressive advances in generative models for sound, text and images. In this talk, I will look into applications of generative models to Lattice QCD. The models I will consider are flows, which are families of diffeomorphisms transforming simple base distributions into complicated target distributions. Traditional ML flows are on vector spaces, which is different from our setup where we need to deal with products of SU(N). I will give details on how we built these flows, and explain how known symmetries of LQCD can be incorporated into them.

In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and C-algebraic quantisation, or strict quantisation, does therefore not deal with such operators. In this talk, I will show how to remedy this problem for Lie-Poisson manifolds (this includes dual of Lie algebras and cotangent bundle of manifolds). As an application, I will show with an example how the quantisation of the dual of the Lie algebroid associated to a Poisson manifold can lead to a quantisation of the Poisson manifold itself. The example I consider is the torus with constant symplectic structure, in which case I recover its usual C-algebraic quantisation.