ICTS

In this talk, we revisit an earlier conjecture by Govindarajan that related conjugacy classes of M_12 to Jacobi forms of weight one and index zero. We construct Jacobi forms for all conjugacy classes of M_12 that are consistent with constraints from group theory as well as modularity. However, we obtain 1427 solutions that satisfy these constraints (to the order that we checked) and are unable to provide a unique Jacobi form. Nevertheless, as a consequence, we are able to provide a group theoretic proof of the evenness of the coefficients of all EOT Jacobi forms associated with conjugacy classes of M_{12}:2 which is subset M_24. In the absence of a unique answer for M_12, we show that there exist moonshines for two distinct L_2(11) sub-groups of the M_12. We also show that BKM Lie superalgebras are associated with one of the L_2(11) sub-groups.