Moonshine at Landau-Ginzburg points

Abstract

We formulate a conjecture predicting unexpected relationships among the coefficients of the elliptic expansions of Klein's modular j-function around j = 0 and j = 1728. Our conjecture is inspired by recent developments in mirror symmetry, in particular by work of Tu computing categorical enumerative invariants of matrix factorization categories and by work of Li-Shen-Zhou computing FJRW invariants of elliptic curves.