$CP$ vioaltion searches in the charm sector at LHCb

LHCb has collected the world's largest sample of charmed hadrons, thus enabling measurements of direct and indirect CP violation parameters of D^0 mesons to be made with unprecedented precision. The difference in CP asymmetries between the singly Cabibbo-suppressed (SCS) D^0 -> K+K- and D^0 -> pi+pi- decays (Delta A_CP) has emerged as a powerful observable to search for direct CPV in the charm sector. By taking the difference between the two modes, most of the asymmetries induced by the detector or coming from the production mechanism are cancelled. The measurement of Delta A_CP done at LHCb is the most precise measurement of a time-integrated CP asymmetry in the charm sector from a single experiment, with a precision reaching the sub-permille level. Two independent measurements of Delta A_CP based on complementary data sets will be presented. Related 2-body searches and searches for direct CP violation in multi-body decays of the D^0 mesons will be discussed. Indirect CP violation in charm is measured through the observable A_Gamma, defined as the time-dependent asymmetry in the decay rates of the SCS D^0 -> h+h- decays. Two independent measurements carried out at LHCb, based on two complementary data sets, will also be presented. Finally, prospects for CP violation searches with Run 2 data and beyond will be discussed.