Gamma conjecture for rank one Fano threefolds

We report on joint work in progress with Don Zagier. Gamma conjecture
I is said to hold for a Fano variety F if the limits of the ratios of
certain solutions to the quantum differential equation of F give the
components of the gamma class of F. We will show how one can prove the
gamma conjecture for rank one Fano threefolds using modular methods.