  Let $W$ be a quasi-homogeneous polynomial of general type and $<J>$ be the
cyclic symmetry group of $W$ generated by the exponential grading element $J$.
We study the quantum spectrum and asymptotic behavior in Fan-Jarvis-Ruan-Witten
theory of the Landau-Ginzburg pair $(W, <J>)$.
  Inspired by Galkin-Golyshev-Iritani's Gamma conjectures for quantum
cohomology of Fano manifolds, we propose Gamma conjectures for
Fan-Jarvis-Ruan-Witten theory of general type. We prove the quantum spectrum
conjecture and the Gamma conjectures for Fermat homogeneous polynomials and the
mirror simple singularities.
  The Gamma structures in Fan-Jarvis-Ruan-Witten theory also provide a bridge
from the category of matrix factorizations of the Landau-Ginzburg pair (the
algebraic aspect) to its analytic aspect. We will explain the relationship
among the Gamma structures, Orlov's semiorthogonal decompositions, and the
Stokes phenomenon.
