Szemer\'edi--Trotter-type theorems in dimension 3
  We estimate the number of incidences in a configuration of $m$ lines and $n$ points in dimension 3. The main term is $mn^{1/3}$ if we work over the real or complex numbers but $mn^{2/5}$ over finite fields. Both of these are optimal, aside from a multiplicative constant that is at most 5. 
J\'anos Koll\'ar (Princeton Univ)
math.CO math.AG