Summer School: Mathematics of Large Networks
The Mathematics of Large Networks Summer School is part of the Large networks and their limits (2022 Spring) semester. This summer school aims to bring together mathematicians and network scientists to foster the exchange of ideas between these two fields. During the school four minicourses will be given by distinguished researchers in graph theory and network science for students from both fields, who are interested in multidisciplinary approaches to networks. The main topics of the summer school include geometry of networks, dynamics on/of networks, higher order structures, network inference and applications.
- Ginestra Bianconi (Queen Mary University of London)
- Remco van der Hofstad (TU Eindhoven)
- Renaud Lambiotte (University of Oxford)
- Kavita Ramanan (Brown University)
- Remco van der Hofstad: Local and global structure of random graphs and complex networks
Abstract: Empirical findings have shown that many real-world networks share fascinating features. Indeed, many real-world networks are small worlds, in the sense that typical distances are much smaller than the size of the network, and are scale-free, in the sense that there is a high variability in the number of direct connections of the elements in the network.
Spurred by these empirical findings, many models have been proposed for such networks. In this lecture series, we discuss empirical findings of real-world networks, and describe some of the random graph models proposed for them, such as the classical Erdös-Rényi random graph, as well as the more relevant configuration model, generalized random graphs and preferential attachment models.
We discuss local convergence in random graphs, and its relation to branching process approximations in, or the locally tree-like nature of, random graphs. While local convergence is related to the local structure around typical vertices in random graphs, it also has indirect implications for many global quantities such as the giant component and small-world properties of random graphs. For example, we show how the statement that the `giant component is almost local' can be made precise, and how it can be related to the small-world nature of random graphs.
Outline of the lecture series:
Lecture 1: Real-world networks and random graphs
Lecture 2: Local convergence of random graphs
Lecture 3: The giant in random graphs is almost local
This lecture series is based on joint work with, amongst others:
Gerard Hooghiemstra, Shankar Bhamidi,
Júlia Komjáthy, Piet Van Mieghem,
Henri van den Esker, and Dmitri Znamenski.
- Kavita Ramanan: Dynamics on Sparse and Heterogeneous Networks
Abstract: We will outline some of the challenges that arise in the study of dynamics on sparse and heterogeneous networks and describe recently developed theory that allows one to provide approximations to empirical measure and marginal network dynamics that are provably accurate in a suitable asymptotic regime. We will also provide illustrative examples of insights that can be gained from these approximations, and discuss several open problems.
A limited number of participants will also get a chance to give a short talk about their work.
Application is now open. Application deadline: 2022 February 1.
The school covers full lodging for all accepted participants at the CEU Conference and Residence Center (H-1106 Budapest, Kerepesi út 87.). There is very limited funding for travel support. Please indicate in the application form if you wish to apply for this support.
MSc and PhD students applying for the summer school should also ask their supervisor to send a short recommendation (typically a few sentences) to the contact e-mail address email@example.com
Link to the registration web-form of the Summer School: