A Conjecture on Maurer–Cartan Element

Gaitto–Moore–Witten studied the infrared algebra (Webb algebra) arising from the TFT. Later, Kapranov–Kontsevich–Soibelman reconstruct this Webb algebra as the $A$ infinity algebra building from the second polytope structure of polyhedral. It was conjectured that one Maurer–Cartan element of this algebra can be obtained from the Fukaya category of Landau–Ginzburg model built from Witten equation. The latter Fukaya category was built by Jiang, Yang and I in 2018. I will introduce the progress of the related problems.