
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.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/158