Leírás
Előadó: Elek Gábor
Cím: Qualitative Graph Limits. Does Deterministic Randomness Exist?
Absztrakt: A sequence of finite, bounded degree graphs converges in the "naive" qualitative sense, if any rooted ball is contained either in all but finitely many of the graphs, or in none but finitely many graphs. If the graphs are Schreier graphs the natural limit objects are the "qualitative" analogues of the IRS's (closed invariant subsets of the space of subgroups).
However, the "real" qualitative convergence notion is the analogue of the local-global convergence. Then, the limit objects are continuous actions of finitely generated groups on Cantor sets: the "qualitative" analogues of measure preserving actions. I will show how much the qualitative theory resembles (or sometimes differs from) the classical "quantitative" local-global convergence theory. I also try to answer the silly-looking question in the title.