Automorphisms of Graphons


April 27, 2015


Laci Lovasz


Eötvös Loránd University


Convergent dense sequences of graphs and their limit objects called graphons were introduced by Borgs, Chayes, Lovasz, Sos, Szegedy and Vesztergombi. Many directions of study of finite graphs extend to the study of graphons, and often yield interesting, even surprising results. In this talk we discuss the automorphism group of graphons. We prove that after an appropriate “standardization” of the graphon, the automorphism group is compact. Furthermore, we characterize the orbits of the automorphism group on k-tuples of points. Among applications we study the graph algebras defined by finite rank graphons and the space of node-transitive graphons.

This is joint work with Balazs Szegedy.


Laci Lovasz

László Lovász was born on March 9, 1948 in Budapest, Hungary. He is married, has 4 children. He obtained his doctoral degree in mathematics from the Eötvös Loránd University, in Budapest, Hungary in 1971. He is a member of the Hungarian Academy of Sciences, the US National Academy of Sciences and several other Academies.

He held the Chair of Geometry at the University of Szeged (1975-1982) and the Chair of Computer Science at the Eötvös Loránd University (Budapest, 1983-1993). He was A.D.White Professor-at-Large at Cornell University (1982-1987), Professor of Mathematics and Computer Science at Yale University (1993-1999), Senior/Principal Researcher at Microsoft Research (1999-2006), Director of the Mathematical Institute of the Eötvös Loránd University (2006-2011), and now the President of the Hungarian Academy of Sciences.

His awards include the George Polya Prize (1979), the Ray D.Fulkerson Prize (1982), the Brouwer Medal of the Dutch Mathematical Society (1993), the Wolf Prize (1999), the Knuth Prize (1999), the Gödel Prize (2001), and the Kyoto Prize (2010). He is editor-in-chief of Combinatorica and editor of 12 other Journals.

His field of research is discrete mathematics, in particular its applications to the theory of algorithms and the theory of computing, and its interactions with classical mathematics. He wrote 5 research monographs and 4 textbooks, and over 250 research papers.