MONSTROUS MOONSHINE OVER $mathbb{Z}$? (Research on algebraic combinatorics and representation theory of finite groups and vertex operator algebras)

Monstrous Moonshine was extended in two complementary directions during the 1980s and 1990s, giving rise to Norton's Generalized Moonshine conjecture and Ryba's Modular Moonshine conjecture. Both conjectures have been unconditionally established in the last few years, so we describe some speculative conjectures that may extend and unify them