Are there very famous open problems or conjectures in representation theory, or in enumerative geometry, like the volume conjecture in topology?



Conjectures and open problems in representation theory
The [Clemens conjecture](https://en.wikipedia.org/wiki/Enumerative_geometry#Clemens_conjecture) in enumerative geometry: a general quintic threefold has only finitely many rational curves in each positive degree.


