Moonshine at Landau-Ginzburg points
Andrei Caldararu, Yunfan He, Shengyuan Huang

TL;DR
This paper conjectures new relationships between the coefficients of Klein's modular j-function expansions around special points, inspired by mirror symmetry and categorical invariants in mathematical physics.
Contribution
It introduces a novel conjecture linking elliptic expansion coefficients of Klein's j-function at j=0 and j=1728, inspired by recent advances in mirror symmetry and enumerative invariants.
Findings
Proposes a conjecture relating modular function coefficients at special points.
Connects mirror symmetry with properties of Klein's j-function.
Suggests new directions for research in modular forms and mathematical physics.
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry
