# Fundamentals of complex networks: From static towards evolving

## Mini-WORKshop, March 6-8, 2019

**Description:**

The main topic of the mini-WORKshop are fundamentals of the mathematical theory of networks, i.e., characterization of their structure (sparse vs. dense, heavy-tailed degree distributions, stochastic symmetries, scaling limits), with a focus on general theory, but also through discussion of key models used in the modeling of real world networks and their limitations. The aim of the workshop is to identify the relevant new directions for advancing the existing theory of stochastic processes on networks to cover the case of *evolving networks*, for which a mathematical theory is still largely lacking.

**Mini-Courses by:**

- Naoki Masuda (Bristol), "Epidemic processes and random walks on time-varying graphs".
- Driven by a widespread observation that various empirical networks change over time, studies of time-varying graphs (also called temporal networks) have been active in network science and beyond for more than a decade. In this mini-course, I will spend the first quarter (i.e., hour) on introduction of time-varying graphs. The remaining three quarters are devoted to epidemic processes (mostly the susceptible-infected-susceptible model) and random walks on time-varying graphs. Many of these topics await purely mathematical foundations, which I would also like to discuss in the course of my talk.

- Peter Mörters (Cologne), "The contact process on evolving scale-free networks".
- We first discuss basic models of static scale-free networks and explore some basic techniques how to study them. We then explore stationary dynamics of graphs that yield evolving networks. The second part of the talk is devoted to the contact process on evolving scale-free networks. We try to obtain an ad-hoc understanding of its behaviour and then discuss a technique how to obtain upper bounds on the extinction time. We demonstrate how metastable exponents can be used to distinguish phases of different survival strategies for the contact process. The course is based on an ongoing joint project with Amitai Linker (Chile) and Emmanuel Jacob (ENS Lyon).

**Learning sessions**:

- Infection processes on networks.
- Statistical physics on networks.
- Statistical inference of processes on networks.

**Local Organizer:**

**Venue:**

- University of Duisburg-Essen, Faculty of Mathematics.
**Address:**Thea-Leymann-Str. 9, D-45127 Essen, Germany. (Directions)**Room:**WSC-S-U-3.02 (third floor, southern corridor), coffee will be served in WSC-N-3.31

From within Germany, Essen can easily be reached by train. There is also a direct Thalys connection from/to Paris.

The closest (≈20 min by a direct train connection) international airport is Düsseldorf (DUS).

**Registration:**

- Registration deadline has passed.