Skip to main content

Benjamini-Schramm approximation of Groups and Graphings

Objective

Large graphs have become central objects in many fields in the last couple of decades: in neural sciences, network sciences (WWW, graph of webpages), social sciences (Facebook) and molecular biology. The standard way to handle large networks is Property Testing: We check only a small number of vertices picked randomly, and we try to learn the properties of the huge graph from this random sample. The general questions of the proposal are the basic problems in all of these fields: Which properties of a large graph are testable? How can we approximate large graphs by small ones?

The proposal is at the crossroads of the following three fields:
1. Sparse graphs and computer science
2. Dynamics and measured group theory
3. Graph limit theory

We expect a boom in the fields of this proposal similarly to the fields related to Szemeredi's theorem. We expect more applications, since sparse graphs appear more often in real life. Recent breakthrough results in computer science play an important role in the methodology. The proposal focuses on three problems in the research frontier addressing the above phenomena:
1. The construction of a nonsofic group
2. The measurable version of the Lovasz Local Lemma
3. The dynamical von Neumann problem

Kun is an expert in the fields of the proposal. After completing his PhD at the Eotvos University he moved to the USA. He plans to return to Europe after six years at top institutions in North America. The Alfred Renyi Institute is a well-known
center in the fields of the proposal, and one of the leading institutions in discrete mathematics. Kun plans to work with Tardos, the scientist in charge, and Abert, Pyber, Szegedy and Szemeredi at the host.

The project would enrich the mathematical culture of Hungary and the ERA, and lead to mutually beneficial, long-term cooperation between the USA and many European countries. If funded Kun would join the host permanently, so the proposal would help to reverse the brain drain phenomenon.

Call for proposal

FP7-PEOPLE-2013-IIF
See other projects for this call

Funding Scheme

MC-IIF - International Incoming Fellowships (IIF)

Coordinator

RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Address
Realtanoda Street 13-15
1053 Budapest
Hungary
Activity type
Other
EU contribution
€ 184 411,20
Administrative Contact
Tiziana Del Viscio (Ms.)