Umbral moonshine

When Tohru Eguchi, Hirosi Ooguri, and Yuji Tachikawa (2011) computed the first few terms of the decomposition of the elliptic genus of a K3 CFT into characters of the N=(4,4) superconformal algebra, they found that the multiplicities matched well with simple combinations of representations of M24.

In 2012, Cheng, Duncan & Harvey (2012) amassed numerical evidence of an extension of Mathieu moonshine, where families of mock modular forms were attached to divisors of 24.

After some group-theoretic discussion with Glauberman, Cheng, Duncan & Harvey (2013) found that this earlier extension was a special case (the A-series) of a more natural encoding by Niemeier lattices.

These minimality properties imply the mock modular forms are uniquely determined by their shadows, which are vector-valued theta series constructed from the root system.

Other moonlight-related words like 'lambency' were given technical meanings (in this case, the genus zero group attached to a shadow SX, whose level is the dual Coxeter number of the root system X) by Cheng, Duncan, and Harvey to continue the theme.