Helly's theorem for systolic complexes
  We prove the analogue of Helly's theorem for systolic complexes. Namely, we show that 7-systolic complexes have Helly dimension less or equal to 1, whereas 6-systolic complexes have Helly dimension bounded from the above by 2. 
Krzysztof \'Swi\k{e}cicki
math.GR math.CO