Differential operators and relations between G-structures

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Here is a non-exhaustive list of questions that will be part of the applicant's research in the following years. For some of them, where a collaboration has already begun or is close to become concrete, I indicate it. Of course, this does not exclude cooperation with other scientists on the corresponding topics.The main questions that this project is aiming to answer are:(1) Find geometric constructions that connect two different types of G-structures, analoguousto the Fefferman construction, linking CR- to conformal geometry. ...(2) Construct linear versions of the Cartan connection (known in the literature as tractor connections) as natural extensions of some invariant differential operators. ...(3) Characterize solutions of some linear differential operators using the prolongation procedure;find vanishing criteria for compact manifolds. ...(4) Consider G-structures on singular spaces (mainly on orbifolds). ...