Mirror symmetry for exceptional unimodular singularities.

In this paper, we prove the mirror symmetry conjecture between the Saito--Givental theory of exceptional unimodular singularities on the Landau--Ginzburg B-side and the Fan--Jarvis-- Ruan--Witten theory of their mirror partners on the Landau--Ginzburg A-side. On the B-side, we develop a perturbative method to compute the genus-0 correlation functions associated to the primitive forms. This is applied to the exceptional unimodular singularities, and we show that the numerical invariants match the orbifold-Grothendieck--Riemann--Roch and WDVV calculations in FJRW theory on the A-side. The coincidence of the full data at all genera is established by reconstruction techniques. Our result establishes the first examples of LG-LG mirror symmetry for weighted homogeneous polynomials of central charge greater than one (i.e. which contain negative degree deformation parameters). [ABSTRACT FROM AUTHOR]