Continuum percolation and random geometric graphs are closely related topics that started over half a century ago with the pioneering work of E.N. Gilbert. The objects of study are mathematical network models whereby a network is formed on random points in the plane (or some higher dimensional space) by connecting pairs of points according to some geometric rule. The points are generated according to some random process such as the Poisson point process; and an example of a rule is to connect two points if their distance is less than some parameter r.

Such models have been the subjects of sustained research effort over the past five decades. In recent years, interest in the topic has heightened because of its relevance to real-world networks such as ad-hoc wireless networks. The topic is currently receiving considerable attention from the mathematics, computer science, and engineering communities. As a result, there is a growing body of impressive results that give a detailed description of several aspects of these models. Notwithstanding this, several challenging questions are left wide open (the most famous one without a doubt being the value of the "percolation threshold" for even the most simple versions of the model in two-dimensions), and novel directions for research continue to be uncovered.

Continuum percolation and random geometric graph theory till now have mainly been built over spaces with a Euclidean geometry. One relatively new and unexplored research direction is the study of models defined instead in the hyperbolic plane or in some other non-Euclidean space. Hyperbolic versions of continuum percolation/random geometric graphs have amongst other things been suggested as good models for social networks, and are also being studied in connection with the routing of messages on a network. The results obtained so far on these hyperbolic models show a behaviour that is spectacularly different from that of their ordinary, Euclidean counterparts. An example of a striking difference is that in hyperbolic percolation models there is often a range of the parameters where infinitely many infinite clusters of points will exist, while in Euclidean models there is never more than one infinite cluster. Given that different research groups in various parts of the world have recently started pursuing results in this direction, the workshop seems particularly well-timed as an occasion for the cross-pollination of research directions, the establishment of new collaborations and the exchange of tools and techniques.

Furthermore, percolation theory, random graph theory, and modelling complex networks are topics that have a strong presence in Canada. The workshop aims to produce a synergy between the researchers in random graphs and those versed in the analysis of largescale networks. For some historical reasons Canada is a stronghold of both fields, with several groups and individuals spread around the country. Several leading experts in these fields are based in Canada and we expect that they, as well as the junior researchers they supervise, will attend the proposed workshop. Having the workshop take place in Toronto is thus certainly very advantageous, not only for the participants from abroad but also for the Canadian scientific community, as a welcome stimulus to an active area of research.

The main goals of the workshop are to facilitate the exchange of tools, techniques, questions, and ideas that will lead to a better understanding of (hyperbolic) continuum percolation/random geometric graphs; and to form new (international) collaborations for the exploration of this exciting research frontier. The workshop will be considered a success if by the end of the workshop some new international joint research projects have been seeded, and if overall the participants have gained a deeper perspective on the behaviour of non-Euclidean continuum percolation/random geometric graphs, as well as the introduction of new geometric models, and can continue to push the field further forward. The aim of the workshop is to bring together researchers from various places in the world and from different communities working on continuum percolation, random geometric graphs, and modelling self-organizing networks. A particular focus of the workshop will be on non-classical models of RGG, e.g. non-Euclidean, soft or dynamic models, but of course there will also be plenty of scope for work on the traditional models.

Registration

This event has reached capacity and registration is now closed.

Funding Requests

This event is not accepting applications for funding/travel support.

Banquet Information

A banquet dinner will be held at Sidecar restaurant on Wednesday, June 21 at 6:00PM. There will be a Prix Fixe menu, which can be found here. Participants can choose to attend the banquet by opting-in on the registration form. The cost is $40 per participant, and includes taxes, water, coffee, and gratuities.