Joint IAS/Princeton University Symplectic Geometry Seminar

I will discuss some results, some older and some newer, on the general idea that in many birationally-Fano cases, generators of the Fukaya category seem to arise from transitions in the minimal model program. A specific result from a couple of years ago, joint with Gonzalez, is that the number of non-displaceable Lagrangian tori in a smooth projective toric variety is at least the number of transitions in a toric minimal model program. A newer specific result is that the blow-up of a smooth projective Fano variety at a finite set contains non-displaceable Lagrangian tori of number at least the order of the set, for sufficiently small exceptional divisor. In general one can show that mmp transitions give rise to non-displaceable Lagrangians under some restrictive hypotheses.