Speaker: Prof. Remco van der Hofstad, Eindhoven University of Technology
Venue: Ramanujan Hall, Dept. of Mathematics, IIT-Bombay
Registration Form: Link
Google Meet link: https://meet.google.com/twf-trww-fnf
Relevant Page: https://www.ieor.iitb.ac.in/node/3967
Lecture Title: Network Science: Structure and Function
Date: 24-25 November, 2025
Time: 14:30 – 17:00
Abstract:
Many phenomena in the real world can be phrased in terms of networks. Examples include the World-Wide Web, social interactions and Internet, but also the interaction patterns between proteins, food webs and citation networks. Many large-scale networks have, despite their diversity in backgrounds, surprisingly much in common. Many of these networks are small worlds, in the sense that one requires few links to hop between pairs of vertices. Also the variability of the number of connections between elements tends to be enormous, which is related to the scale-free phenomenon.
In this lecture series, we describe a few real-world networks and some of their empirical properties. We also describe the effectiveness of abstract network modelling in terms of graphs, and how these models help us to make sense to the empirical findings. We continue by discussing some random graph models for real-world networks and their properties, as well as their merits and flaws as network models. We further discuss the implications of some of the empirical findings on information diffusion, such as the spread of fake news, and competition on such scale-free networks, as well as the local and `almost local' structure of random graphs.
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Colloquium Title: Surprises in percolation on random graphs
Date: 26 November, 2025
Time: 14:30 – 15:30
Abstract:
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light, connectivity is hardly affected. We study the location and nature of the phase transition on random graphs. In particular, we focus on the connectivity structure close to, or below, criticality, where components display intricate scaling behaviour such that a typical connected component has a bounded size, while the maximal connected component sizes grow like powers of the network size.
We review the recent progress that has been made on percolation on random graphs whose expected adjacency matrix is close to being rank-1, the most prominent examples being the configuration model and rank-1 inhomogeneous random graphs. Time permitting, I will also discuss the surprising phase transition on dynamic random graphs, i.e., random graphs that grow with time, such as uniform attachment models. Remarkably, these two settings behave rather differently. In all cases, the inhomogeneity of the underlying random graph on which we perform percolation is of crucial importance.
In my presentation, I focus on the surprising behaviour of percolation on random graphs with infinite-variance degrees, and on growing random graphs.
[This is joint work with Sayan Banerjee, Shankar Bhamidi, Souvik Dhara, Rajat Hazra, Johan van Leeuwaarden, and Rounak Ray.]
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Biography:
Remco van der Hofstad received his PhD at the University of Utrecht in 1997, under the supervision of Frank den Hollander and Richard Gill. Since then, he worked at McMaster University in Hamilton, Canada, and Delft University of Technology. Since 2005, he is full professor in probability at Eindhoven University of Technology. Remco was scientific director of Eurandom from 2011 until 2019, and jointly with Frank den Hollander he is responsible for the `Random Spatial Structures' Program at Eurandom. He wrote close to 200 papers, and three books on random graphs, complex networks, and high-dimensional percolations (the latter with Markus Heydenreich).
Remco received the Rollo Davidson Prize 2007, and is a laureate of the `Innovative Research VIDI Scheme' 2003 and `Innovative Research VICI Scheme' 2008. He is also one of the 11 co-applicants of the Gravitation program NETWORKS (see https://www.thenetworkcenter.nl/ for more information). In 2018, Remco was elected in the Royal Academy of Science and Arts (KNAW), where he currently is the chair of the Mathematics Section and member of the Board Natural and Technical Sciences.
Remco is editor in chief of the `Network Pages', an interactive website by the networks community for everyone interested in networks (see https://www.networkpages.nl/ for more information). Remco is contact person for the research area Grip on Complexity of the Institute for Complex Molecular Systems. He is also the chair of the Board of Trustees of the Applied Probability Trust, and member of the Steering Committee of the Dutch NetSci chapter.