  The Gamma-class is a characteristic class for complex manifolds with
transcendental coefficients. It defines an integral structure of quantum
cohomology, or more precisely, an integral lattice in the space of flat
sections of the quantum connection. We present several conjectures (the
Gamma-conjectures) about this structure, particularly focusing on the
Riemann-Hilbert problem it poses. We also discuss a conjectural functoriality
of quantum cohomology under birational transformations.
