Tropically Unirational Varieties
  We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether all unirational varieties are tropically unirational. We present several techniques for proving tropical unirationality, along with various examples. 
Jan Draisma, Bart Frenk
math.AG math.CO