CS294-179: NETWORK STRUCTURE AND EPIDEMICS, FALL 2020

INSTRUCTOR: Christian Borgs (borgs@eecs)
TIME: Tuesday, Thursday 2:30-4:00
PLACE: Online (Zoom)
OFFICE HOURS: Online, TBD

RECENT ANNOUNCEMENTS

COURSE DESCRIPTION

Networks play a central role in our social and economic lives. They affect our well-being by influencing the information we receive, products we choose to buy, economic opportunities we enjoy, and diseases we catch from others. How do these networks form? Which network structures are likely to emerge in society? And how does the structure of the network impact the dynamics of the spread of an innovation or infection.

This course tries to survey the mathematical results developed in the last few years on analyzing the structure of popular random networks, as well as the understanding of processes on them, with particular emphasis on epidemics. In addition it will touch on a recently very popular subject, the non-parametric modeling of a large graph via a graphon, and the related notion of graph limits.

The course is loosely based on the text book “Random Graph Dynamics” by Rick Durrett, updated to what has happened since its publication, including the topics of graphons and graph limits, plus a larger emphasis on epidemics, as well as a short introduction to the topic of the spread of information and innovation. Additional literature, including original research papers, will be provided during the course.

Prerequisites:

The course is open to graduate students with a good level of mathematical maturity and a strong background in probability (including some knowledge of Martingales, Markov Chains, and basic notions of stochastic processes), as well as some basic background in graph theory and differential equations.

Tentative List of Topics

Random Graph Models and Structure of Large Networks (50-60%): Epidemics Models and their Behavior (about 25%): Algorithmic Aspects (20-25%)

ATTENDANCE, ASSIGNMENTS, ETC.:

The course will be online, and I hope for active participation of everyone enrolled. Therefore attendance is mandatory, and will be part of the assessment.

I will periodically give problem assignments, for which I encourage collaboration of 2-3 students, but expect separately written up solutions from every participant.

Depending on the size of the class, part of the course may be a final project done in groups of a few. These projects would involve the reading and deep understanding of a research paper, writing up what you learned, plus something “extra”, which can range from a simulation demonstrating or visualizing some of the results of the paper(s), to working out some part which in the paper was “left to the reader”, to solving an unsolved research problem.

LECTURE NOTES

HOMEWORKS