Ultrametric Logarithm Laws I
  We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are S-arithmetic Diophantine approximation results and logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on trees. 
Jayadev S. Athreya, Anish Ghosh, and Amritanshu Prasad