Recent progress on the distribution of rational and integral points on homogeneous varieties 

In this talk I'll give a survey of some works studying the distribution of rational points on compactifications of semisimple groups. Time allowing, I'll state a conjecture about the distribution of Campana points on Fano varieties and discuss some evidence using homogeneous varieties.  The newer results in this talk are joint work with Demirhan, Chow-Loughran-Tanimoto, and Tanimoto-Tschinkel.