We propose to study some features in two settings where the pure spinor formalism has proven to be efficient. In first place, when computing multiloop amplitudes in the non-minimal version of the pure spinor string, there appear some issues related to an increasingly divergent amplitude integrand as we go higher in the number of loops. The divergence occurs in the region near the pure spinor cone apex, and it comes from negatives powers on these variables. Then, we pretend to take some steps towards one way of regularizing these expressions. In second place, some progress has been made in the construction of half-BPS vertex operators in AdS using pure spinor variables. Even at large radius (flat space limit), delta functions of pure spinor varibles are used but treated formally. We expect to generalize Belopolsky's treatment of the delta function and its derivatives that (used to construct picture changing operators) to admit constrained variables such as the pure spinor ones.
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