  The quantum Hall effect in curved space has been the subject of many
theoretical investigations in the past, but devising a physical system to
observe this effect is hard. Many works have indicated that electronic
excitations in strained graphene realize Dirac fermions in curved space in the
presence of a background pseudo-gauge field, providing an ideal playground for
this. However, the absence of a direct matching between a numerical, strained
tight-binding calculation of an observable and the corresponding curved space
prediction has hindered realistic predictions. In this work, we provide this
matching by deriving the low-energy Hamiltonian from the tight-binding model
analytically to second order in the strain and mapping it to the curved-space
Dirac equation. Using a strain profile that produces a constant pseudo-magnetic
field and a constant curvature, we compute the Landau level spectrum with
real-space numerical tight-binding calculations and find excellent agreement
with the prediction of the quantum Hall effect in curved space. We conclude
discussing experimental schemes for measuring this effect.
