Applications of Nevanlinna's vlaue distribution theory to functional equations and related conjectures

It's well known that Nevanlinna's value distribution theory is the most useful, powerful and effective tool in dealing with the functional equations of meromorphic functions. In the talk, some unsolved old and new conjectures (mainly posed by the speaker over past decades) that related to admissible meromorphic solutions of functional equations of various types, including differential and difference equations as well as Fermat type of equations ,along with the background and progresses of these conjectures will be surveyed or reported, for further studies.