Scaling Limits of Dynamical Processes on Random Graphs (19w5071)


Grzegorz Rempala (The Ohio State University)

(Duke University)

(Technische Universitat Darmstadt)

(Eindhoven University of Technology)


The Casa Matemática Oaxaca (CMO) will host the "Scaling Limits of Dynamical Processes on Random Graphs" workshop in Oaxaca, from May 19, 2019 to May 24, 2019.

The field "dynamical processes on networks'' is the marriage of two diverse disciplines that have long been studied independently. With the overwhelming proliferation of social networks, never has it been more important to understand and model the spread of rumour, the dissemination of propaganda, or the very behaviour of social networks in general, which is often quite complex and adaptive. As our dependence on computer networks grows, so does the need to better understand and prevent spread of computer viruses. Similarly, incorporating network structure and studying its impact on various epidemic process is also the need of the hour.

In this workshop, we wish to focus on scaling limits of such systems as the size of the network grows arbitrarily large. For instance, we ask questions like "can we approximate such a limiting process by a simpler mathematical description? If so, under what conditions? How does the structure of the network, in particular the degrees in the network, impact the limiting process? Is the degree distribution sufficient to describe the limiting process? If there are two or more competing processes such as infectious diseases, which one will eventually pervade the entire graph? Is steady co-existence of two or more competing processes possible? If so, for which class of random graphs? Numerous other extensions are feasible and relevant.

The topic "scaling limits of dynamical processes on random graphs'' is of interest to mathematicians, epidemiologists, physicists, computer scientists and engineers. The main objective of this workshop is to consolidate results developed by different communities into a comprehensive and mathematically rigorous body of work. The workshop is also expected to foster new collaboration among these different communities.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT