Recently, Connes, Consani and Moscovici in https://arxiv.org/abs/2310.18423 have blended two of their results on zeta zeros and the prolate wave operators, which, they say, "suggests the tantalizing program of finding the semilocal analogue of the prolate operator. With such operator-theoretic tools in the semilocal case one could deal with Weil’s positivity".
They in particular study semilocal Sonin spaces and say that it "suggests that the obtained invariantly defined Sonin space should, when suitably equiped with a prolate type operator, play the role of the sought for Weil cohomology".
The paper presents a candidate for the semilocal analogue of the prolate operator while another candidate linked to the metaplectic representation of the cover of a certain algebraic group is announced for a forthcoming paper.
Apparently these results were presented at a workshop at the Fields Institute last week http://www.fields.utoronto.ca/activities/23-24/operator-noncommutative
Questions: at the level of a beginning graduate student :
A) what is the Weil cohomology?
B) (judgemental, but hopefully not in a bad way), just to have an idea, does it feel like RH is in sight?
