Givental-type reconstruction at a non-semisimple point

Out of all cohomological field theories (CohFT for brevity) the best understood are so-called semisimple CohFTs, for which one can compute Givental’s group element whose action on the tensor product of several Gromov-Witten theories of a point is exactly the CohFT given. One says then that this Givental’s group element reconstructs the CohFT. However this is only applicable to semisimple CohFTs. This talk deals with the Givental-type reconstruction without semisimplicity. We show it for one particular example of the certain orbifold Gromov-Witten theory. To achieve the result we first solve modern mirror symmetry conjecture about CY/LG correspondence. In this sense this talk could be seen as an application of mirror symmetry results to the more classical problems