Mirror symmetry between Landau-Ginzburg models

LG models together with Calabi-Yau models form the global picture of mirror symmetry. In mathematics, LG A theory relates to the quantum singularity theory built by Fan-Jarvis-Ruan based on Witten's work on r-spin curves, while the LG B model relates to Saito's primitive form theory and the subsequent quantization theories of Givental or Dubrovin-Zhang. In this talk, I will explain the mirror correspondence between the two theories. If time permits, I will discuss other problems.