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I have been reading this recent paper of J.McKay and YH. He (they've written a number of papers recently, including a fun and joking one on 42 which overflow commented on) called "Sporadic and Exceptional"

http://arxiv.org/abs/1505.06742

There are some old ideas which are summarized and some new observations and numerology. Whatever it is, it seems like some kind of over-arching set of correspondences linking Monster/Baby/Fischer versus E8/E7/E6, i.e., the largest sporadic groups versus the largest simple exceptional Lie algebras, using cusp numbers and enumerative problems on del Pezzo surfaces.

However, numerology aside. Anyone have any ideas/comments on how to find the geometric significance of the cusps and why they are relevant to Moonshine and to this current context?

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