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The Elementary Theory of Partially Commutative Groups (PCG)
Start date: Sep 1, 2014, End date: Aug 31, 2019 PROJECT  FINISHED 

"The solution of Tarski's problems on the first-order theory of freegroups has uncovered deep connections between Model Theory, Geometryand Group Theory and served as a nexus and motivation for manyclassical results in Geometric Group Theory and Theoretical ComputerScience.Just as the Tarski problems connected the theory of free groups withthe geometry of trees, our goal is to point at a new direction inGroup Theory and develop appropriate generalisations of the techniquesand results whose nature is based on the geometry of higherdimensional counterparts of trees and interplays with the theory ofpartially commutative groups, notably the theory of groups acting onreal cubings.We then shall apply these tools to approach fundamental questions inthe model theory of partially commutative groups: classify finitelygenerated groups elementarily equivalent to a given partiallycommutative group and prove decidability and stability of theirfirst-order theory."
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