Context : While rotation has a major impact on stellar structure and evolution , its effects are not well understood .
Thanks to high-quality and long timebase photometric observations obtained with recent space missions , we are now able to study stellar rotation more precisely .

Aims : We aim to constrain radial differential rotation profiles in \gamma Doradus ( \gamma Dor ) stars , and to develop new theoretical seismic diagnosis for such stars with rapid and potentially non-uniform rotation .

Methods : We derive a new asymptotic description which accounts for the impact of weak differential near-core rotation on gravity-mode period spacings .
The theoretical predictions are illustrated from pulsation computations with the code GYRE and compared with observations of \gamma Dor stars .
When possible , we also derive the surface rotation rates in these stars by detecting and analysing signatures of rotational modulation , and compute the core-to-surface rotation ratios .

Results : Stellar rotation has to be strongly differential before its effects on period spacing patterns can be detected , unless multiple period spacing patterns can be compared .
Six stars in our sample exhibit a single unexplained period spacing pattern of retrograde modes .
We hypothesise that these are Yanai modes .
Finally , we find signatures of rotational spot modulation in the photometric data of eight targets .

Conclusions : If only one period spacing pattern is detected and analysed for a star , it is difficult to detect differential rotation .
A rigidly rotating model will often provide the best solution .
Differential rotation can only be detected when multiple period spacing patterns have been found for a single star or its surface rotation rate is known as well .
This is the case for eight stars in our sample , revealing surface-to-core rotation ratios between 0.95 and 1.05 .