Quantum singularity theory (FJRW) and the generalized Witten conjecture

I will explain the quantum singularity theory (FJRW) built by Fan-Jarvis-Ruan based on Witten's r-spin curve theory
and simply describe the proof of the generalized Witten conjecture for ADE singularities. Quantum singularity theory
is another cohomological field theory besides Gromov-Witten theory and is the mathematical description of the
Landau-Ginzburg A model.