A Reduction of the F-Conjecture

The long-standing F-Conjecture asserts that there is a very simple description for the closed cone of effective curves on the moduli space M_{g,n}\bar of stable n-pointed curves of genus g as being determined by a finite collection of so-called F-curves. In my talk,  I will explain how the F-Conjecture can be reduced to a simple problem on M_{1,n}\bar involving a relatively small number of F-curves of one particular type, and that this reformulation may be more useful for finding a counterexample than for proving more cases.