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Limit Groups over Partially Commutative Groups

Objective

Klein proposed Group Theory as a means of formulating and understanding geometrical constructions. Geometric Group Theory embraces this approach and also reverses it by using geometrical ideas to give new insights into central problems in Group Theory. In the last decades, it has become a nexus between several branches of mathematics such as Geometry, Model Theory, Dynamical Systems and Algebraic Geometry over Groups.

One of the most representative exponents of this interdisciplinary connection is the theory of limit groups. This theory played a crucial role in the recent solution of the famous Tarski problems and revealed a beautiful and deep relation with the theories of JSJ decompositions and very small actions on real trees.

As the geometry of free groups is associated to trees, the geometry of partially commutative groups is associated to higher-dimensional analogues of trees. Partially commutative groups are not simply generalisations of free groups, they appear naturally in many different branches of mathematics as well as in computer science, robotics and theoretical physics. This project aims at developing a theory of limit groups over partially commutative groups from algebraic, geometric, algorithmic and model theoretic viewpoints. It intends to explore and strengthen the interconnection between the aforementioned branches of mathematics and to open up directions for further research in each of them.

Field of science

  • /natural sciences/physical sciences/theoretical physics
  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/mathematics/applied mathematics/dynamical systems
  • /natural sciences/mathematics/pure mathematics/algebra/algebraic geometry
  • /natural sciences/computer and information sciences

Call for proposal

FP7-PEOPLE-2011-IIF
See other projects for this call

Funding Scheme

MC-IIF - International Incoming Fellowships (IIF)

Coordinator

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
Wellington Square University Offices
OX1 2JD Oxford
United Kingdom
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 200 371,80
Administrative Contact
Gill Wells (Mr.)