  The space experiment CoRoT has recently detected a transiting hot Jupiter in
orbit around a moderately active F-type main-sequence star (CoRoT-Exo-4a). This
planetary system is of particular interest because it has an orbital period of
9.202 days, the second longest one among the transiting planets known to date.
We study the surface rotation and the activity of the host star during an
uninterrupted sequence of optical observations of 58 days. Our approach is
based on a maximum entropy spot modelling technique extensively tested by
modelling the variation of the total solar irradiance. It assumes that stellar
active regions consist of cool spots and bright faculae, analogous to sunspots
and solar photospheric faculae, whose visibility is modulated by stellar
rotation. The modelling of the light curve of CoRoT-Exo-4a reveals three main
active longitudes with lifetimes between about 30 and 60 days that rotate
quasi-synchronously with the orbital motion of the planet. The different
rotation rates of the active longitudes are interpreted in terms of surface
differential rotation and a lower limit of 0.057 \pm 0.015 is derived for its
relative amplitude. The enhancement of activity observed close to the
subplanetary longitude suggests a magnetic star-planet interaction, although
the short duration of the time series prevents us from drawing definite
conclusions.
