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 for a broad audience, we describe a few real-world networks and some of their empirical properties. We also describe the effectiveness of abstract network modeling in terms of graphs and how real-world networks can be modeled, as well as how these models help us to give 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 conclude by discussing the implications of some of the empirical findings on information diffusion and competition on such networks.
We assume no prior knowledge in graph theory, probability or otherwise.
Biography:
Remco van der Hofstad received his Ph.D. 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. He is currently Full Professor in probability at Eindhoven University of Technology and Acting Scientific Director of Eurandom. Further, jointly with Frank den Hollander, he is responsible for the 'Random Spatial Structures' Program at Eurandom.
Remco works on statistical mechanics in high dimensions, on random graph models for complex networks and stochastic processes on them, and the interplay between these topics. He is further interested in exploring applications of probability in chemistry, electrical engineering and computer science with scientists from these fields.
Remco received the Prix Henri Poincaré 2003 jointly with Gordon Slade, the Rollo Davidson Prize 2007, is a laureate of the 'Innovative Research VIDI Scheme' 2003 and 'Innovative Research VICI Scheme' 2008, and was elected in the Royal Netherlands Academy of Arts and Sciences in 2018. He is also one of the 11 co-applicants of the Dutch Gravitation program NETWORKS. This 23 M euro program, a collaboration between the universities of Amsterdam, Leiden and Eindhoven, and the Center for Mathematics and Computer Science in Amsterdam, aims at combining stochastics and algorithmics to solve network problems.
Remco has lectured in most of the major summer schools in probability, including Saint-Flour 2017, Cornell 2012, PIMS-CRM in Montreal 2015, and has taught some 20 more shorter and longer courses throughout the world. He is author of some 130 papers and 2 books, with two more books in preparation. He has supervised 20 Ph.D. students, of whom 15 have completed their Ph.D., and 15 postdocs.
Remco is editor in chief of the 'Network Pages', an interactive website by the networks community for everyone interested in networks.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai