Speaker: Dr. Chung Hang Liu（廖仲行博士）

Time: 10:00-11:00, 29 November 2025 (Saturday) (Beijing time)

Venue: A103, Lijiao Building

Abstract

Bootstrap Percolation is a particular class of cellular automata, and can be viewed as the spread of information on a graph. A large variety of phenomena can be modelled, such as the spreading of beliefs in social networks, financial contagion in economic networks, and the spread of viruses in animal populations. With a vast amount of applications, there have been significant work on bootstrap percolation in recent years, by mathematicians, physicists, sociologists, and computer scientists, among others. A typical model of bootstrap percolation can be described as follows. Suppose that in a very large graph, several vertices are initially randomly infected. At each time step, any uninfected vertex becomes infected if it has at least a certain number of infected neighbours. Any infected vertex stays infected forever. A central question would be, under what circumstances will (almost) all vertices become infected?

In this talk, I will present some results in the subject of bootstrap percolation. A well-studied case is when the graph in question is a high dimensional integer lattice, for which there are results of Aizenman and Lebowitz; Schonmann; Cerf and Manzo; Holroyd; and Balogh, Bollobás, Duminil-Copin and Morris, among others. Among the more recent research, I shall discuss bootstrap percolation on random geometric graphs, for which there are results of Bradonjić and Saniee; Candellero and Fountoulakis; Koch and Lengler; and Falgas-Ravry and Sarkar; and triangle bootstrap percolation on the grid, which was considered by Araujo et al. The techniques in the proofs of the results involve an interesting blend of ideas from probability theory and combinatorics. Several open problems will be mentioned.

About the Speaker

Dr. Henry Liu is an Associate Professor in Mathematics at Department of Mathematical Sciences, Beijing Normal-Hong Kong Baptist University. He received his Ph.D. from The University of Memphis, USA, where his subject of specialization in mathematics is combinatorics. He also holds masters degrees in mathematics from University of Cambridge, UK, and University College London, UK. Dr. Liu has published research papers in many advanced journals, including SIAM Journal on Discrete Mathematics, European Journal of Combinatorics, Journal of Graph Theory, Discrete Applied Mathematics, and Discrete Mathematics. His major research direction is combinatorics, and he is interested in the connections of combinatorics to other subjects in mathematics such as probability theory and discrete geometry, as well as applications of combinatorics to real world problems.