Title: Variation of GIT quotients and combinatorics of GKM graphs.

Annotation: Geometric invariants theory quotients are generalizations of the construction of projective spaces: one takes away a "bad" closed subvariety ("unstable locus") and then takes the quotient in the categorical sense. However, the choice of the "bad" subvariety depends on a polarization (that is a choice of an ample line bundle) and a linearization (that is a group action on the chosen line bundle). Different linearizations produce different quotients that may vary essentially but still are connected to each other through the "wall crossing" procedure. Say, any smooth projectove variety with the action of the 1-dimensional torus with isolated fixed points may be connected to a (weighted) projective space by a sequence of (weighted) flips. We also consider a combinatorial counterpart of this theory introduced by Guillemin and Zara using the language of Goresky-Kottwitz-Macpherson graphs.