The probability of non-existence of small substructures via clusters and cumulants
Speaker: Dr. Rui Zhang
Affiliation: Universitat Pompeu Fabra
Abstract
We study the asymptotic probability of non-existence of small substructures in random objects using tools from cluster expansion and cumulant theory. In particular, we will study the following topics: the non-existence of small subhypergraphs in random hypergraphs, the limiting distribution of maxima of various extension counts in random graphs, and the asymptotic enumeration of Eulerian orientations, Eulerian digraphs, and Eulerian oriented graphs. The content is based on papers with my coauthors: Mikhail Isaev, Brendan McKay, Igor Rodionov, Nick Wormald and Maksim Zhukovskii.
Dr. Rui Zhang is a Postdoc (2023.10-now) under the supervision of Gabor Lugosi at the Statistics Group in the Barcelona School of Economics, Universitat Pompeu Fabra. Before that, he received his Ph.D. in Mathematics (2019.09-2023.12) under the supervision of Nick Wormald and Mikhail Isaev at the Discrete Mathematics Group from Monash University. His interests include probabilistic combinatorics and random structures.
About Pure mathematics seminars
We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.
Seminars are usually held on Tuesdays from 2 to 3pm.
Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.
Information for speakers
Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.
Contact us
To volunteer to talk or to suggest a speaker, email Ole Warnaar or Ramiro Lafuente.
Venue
Room: 442