Moduli spaces of d-connections and difference Painleve equations
  We show that difference Painleve equations can be interpreted as isomorphisms of moduli spaces of d-connections on the projective line with given singularity structure. We also derive a new difference equation. It is the most general difference Painleve equation known so far, and it degenerates to both difference Painleve V and classical (differential) Painleve VI equations. 
D. Arinkin, A. Borodin