Speaker László Lovász
Host Jennifer Chayes
Affiliation Department of Computer Science of the Eötvös Loránd University in Budapest
Date recorded 7 September 2011
It is becoming more and more clear that many of the most exciting structures of our world can be described as large networks. The internet is perhaps the foremost example, modeled by different networks (the physical internet, a network of devices; the world wide web, a network of webpages and hyperlinks). Various social networks, several of them created by the internet, are studied by sociologist, historians, epidemiologists, and economists. Huge networks arise in biology (from ecological networks to the brain), physics, and engineering.
These networks pose exciting and challenging problems for the mathematician: these networks are never completely known, and indeed often not even completely defined. At any time, we can only have partial information about them, through sampling locally, or observing the behavior of some global process.
The approach to the study of such networks includes finding procedures (usually
The limit theory allows us to answer some basic questions both in theory and practice. For example, in extremal graph theory: Which inequalities between subgraph densities are valid? Can these be proved using just Cauchy-Schwarz? is there always and extremal graph, and what is the possible structure of these?
The limit theory has been developed by Borgs, Chayes, Lovasz, Sos, Szegedy and Vesztergombi in the dense case, and by Aldous, Benjamini, Schramm, Elek and others in the sparse case.
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