Since the important Moonshine VOA was constructed by Frenkel, Lepowsky and Meurman in the mid-80s, there has been much interest in relations between
finite groups and VOAs. This connection has inspired new viewpoints about moonshine theories.
My lecture will survey highlights of work on these topics:
Uniqueness results for the Moonshine VOA.
A new (and easier) construction of the Monster, using VOA theory.
Integral forms in VOAs and VAs in positive characteristic (and automorphism groups).
Modular moonshine.
Miyamoto involutions (on VOAs) and $EE_8$ pairs. ($EE_8$ means square
root of 2 times the famous $E_8$-lattice.) Moonshine paths, connecting the extended $E_8$ diagram with dihedral groups in the Monster.
I am grateful for joint work and consultations with Chongying Dong, Ching Hung Lam, Alex Ryba.