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"FINITE DIMENSIONAL APPROXIMATIONS OF GRAPHS, GROUPS AND ALGEBRAS"

Objective

"Finite dimensional approximation phenomenon is laying at the crossroads of graph theory, group theory and operator algebras. It helps to understand constant-time algorithms, von Neumann factors and several interesting conjectures on discrete groups.

In a nutshell, finite dimensional approximation means that certain infinite structures, groups, graphs, measurable equivalence relations or algebras can be regarded as limits of finite or finite dimensional objects.

Using the limit notions one can prove theorems in the finite world by looking at the limits, or prove theorems about infinite groups or infinite dimensional algebras by investigating the finite objects.

The theory (and the proposal itself) is closely related to famous problems such as
the Atiyah Conjecture or the Connes Embedding Conjecture.

Gabor Elek, the researcher in the proposal is an expert of this area and made successful research on various branches of finite dimensional approximation theory such as sofic groups, L2-invariants, profinite actions and hypergraph limits.
He proposes to attack several problems of the area. His ultimate goal is to work out a general theory of the subject and to extend the scope of finite dimensional approximation theory to some new areas of mathematics.

Elek currently holds a senior researcher position at the Alfred Renyi Mathematical
Institute of the Hungarian Academy of Sciences. If funded, he intends to build further connections between the Hungarian combinatorics school and European institutions."

Field of science

  • /natural sciences/mathematics/pure mathematics/algebra
  • /natural sciences/mathematics/pure mathematics/discrete mathematics/graph theory
  • /natural sciences/mathematics

Call for proposal

FP7-PEOPLE-2010-IEF
See other projects for this call

Funding Scheme

MC-IEF - Intra-European Fellowships (IEF)

Coordinator

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Address
Batiment Ce 3316 Station 1
1015 Lausanne
Switzerland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 240 705
Administrative Contact
Nicolas Monod (Prof.)