Real and discrete holomorphy : Introduction to an algebraic approach
  We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is then possible to define an "amazing" notion of holomorphic functions on them, and show how rigid it is in some cases. 
Sylvain Barr\'e (LMAM), Abdelghani Zeghib (UMPA-ENSL)