Network science is a hot and high-impactful area. Critical behaviour in topological random networks is under scrutiny in past decade. Many questions dealing with phase transitions in graphs and networks spread nowadays far beyond the pure academic interest and play crucial role in various branches of physics (structure of membranes, formation of cosmic webs), technology (transport optimization, critical properties of electric networks), and life sciences and medicine (epidemic spread, structure of connectome, analysis of genomic and protein networks). Investigation of critical and collective effects in graphs and networks has becoming a new rapidly developing interdisciplinary area, with diverse applications and variety of questions to be asked. One of the most intriguing questions deals with a design of networks of special topology under evolution, when some control parameters are changing. Many-body interactions, beyond the free-field theory, play crucial role in the network statistics. Presence of such interactions is responsible for emergence of phase transitions in complex distributed systems. Particularly, the classical methods of the theory of complex networks are very useful in neurobiology and in medicine, especially in the context of COVID-19 propagation. At length of our workshop, we plan to focus on statistical and dynamic properties of epidemic networks.
The specific subjects of the workshop are devoted to challenging modern research directions. Despite of variety of applications, there are some common methods of studying critical phenomena in graphs and networks, borrowed from the spectral theory, statistical physics, and physics of condensed matter. During the workshop we plan to provide balanced view of applied research and fundamental methods available to test statistical and dynamic characteristics of systems under consideration. In particular, we plan to focus our attention to the following questions:
The workshop is interdisciplinary. The network science is becoming now the “unifying language” for many branches of physics, computer science, mathematics and biology. The same can be said about particular questions dealing with investigation of criticality and collective behaviour in generic complex systems. The workshop provides a platform where these two directions, networks and criticality, meet each other with a synergetic effect.
The typical total number of participants of CCEGN conference is about 50. This number includes about 20 invited speakers (in average four-five 1-hour talks per day). The venue of Euler Institute and the schedule of the workshop would encourage free informal discussions.
We plan to Involve young researchers in discussions. Specifically, we plan to organize during the workshop few informal groups of interests (for 3-4 hot topics of the workshop) which will attack some preselected educationally-scientific problem and provide the results of their research at the end of the workshop. When inviting participants and scheduling lectures, we plan to balancing interests of all categories of participants.
The workshop will be announced very widely, including postings at news feeds, and social media channels. We expect to attract even more students if posted on the ICM website. The recorded lectures will be available at the web page of the conference and on YouTube, photos of research events and social life during the workshop will be available online on permission of involved participants.
The workshop "Critical and collective effects in graphs and networks" is an official International Congress of Mathematicians 2022 (ICM 2022) Satellite conference. The ICM is the most significant meeting in pure and applied mathematics worldwide, and one of the oldest scientific congresses. ICMs are organized every four years by the International Mathematical Union in partnership with the Local Organizing Committee from the host country. The ICM 2022 will be held in St Petersburg, Russia, 6 - 14 July 2022.