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The Elementary Theory of Partially Commutative Groups

Objective

"The solution of Tarski's problems on the first-order theory of free
groups has uncovered deep connections between Model Theory, Geometry
and Group Theory and served as a nexus and motivation for many
classical results in Geometric Group Theory and Theoretical Computer
Science.

Just as the Tarski problems connected the theory of free groups with
the geometry of trees, our goal is to point at a new direction in
Group Theory and develop appropriate generalisations of the techniques
and results whose nature is based on the geometry of higher
dimensional counterparts of trees and interplays with the theory of
partially commutative groups, notably the theory of groups acting on
real cubings.

We then shall apply these tools to approach fundamental questions in
the model theory of partially commutative groups: classify finitely
generated groups elementarily equivalent to a given partially
commutative group and prove decidability and stability of their
first-order theory."

Field of science

  • /natural sciences/mathematics/pure mathematics/geometry

Call for proposal

ERC-2013-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA
Address
Barrio Sarriena S N
48940 Leioa
Spain
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 021 216,80
Principal investigator
Ilya Kazachkov (Dr.)
Administrative Contact
Charo Sánchez (Ms.)

Beneficiaries (1)

UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA
Spain
EU contribution
€ 1 021 216,80
Address
Barrio Sarriena S N
48940 Leioa
Activity type
Higher or Secondary Education Establishments
Principal investigator
Ilya Kazachkov (Dr.)
Administrative Contact
Charo Sánchez (Ms.)