The centre of the universal enveloping algebra of a complex semisimple Lie algebra has been understood for a long time since the pioneering work of Harish-Chandra. In contrast, the centres of the equivalent notions in characteristic p are still yet to be computed explicitly. In this talk, Zhenyu Yang and Rick Chen will present an explicit basis for the centre of the restricted enveloping algebra of sl_2, constructed from explicit calculations combined with techniques from non-commutative rings and Morita equivalences. They will then explain how to generalise the argument to compute the centre of the distribution algebra of the second Frobenius kernel of the algebraic group SL_2. This work was part of their summer project under the supervision of Konstantin Ardakov.