Our speakers and panelists, who span multiple disciplines, include Rediet Abebe (University of California, Berkeley), Daryl R. DeFord (Washington State University), Sandra González-Bailón (University of Pennsylvania), Elizabeth Munch (Michigan State University), Nancy Rodríguez (University of Colorado, Boulder), Shelby M. Scott (University of Tennessee, Knoxville), Joseph H. Tien (Ohio State University), Chad M. Topaz (Williams College), and Jennifer N. Victor (George Mason University).

The spread of memes and misinformation on social media, political redistricting, pedestrian movement in crowds, and the dynamics of voters during elections are among the many things that people study in the field of complex systems. All of these phenomena involve the interactions of individual parts, which come together to produce rich, complex collective dynamics. Obtaining a better understanding of how these interacting parts–whether they are Twitter accounts, pedestrians, or voters–respond to each other and to their environment also has important implications for society. In this Short Course, we will introduce participants to some of the mathematical and computational techniques that researchers and policy-makers use to shed light on problems in complex systems, with a particular focus on those that arise in social and political settings.

The mathematical study of complex social systems draws on many subfields, including data-driven modeling, data analysis, network science, and topology and geometry. We will overview these mathematical methods, while also equipping participants with associated computational skills and discussing ways of engaging in cross-disciplinary research. We will present and discuss problems that are motivated by public opinion, political elections, social media, and social advocacy. Through a combination of survey lectures, software tutorials, panels, and community-building discussions, our goals are (1) to introduce participants to complex social systems and (2) to engage and mentor people who are interested in pursuing research in this area.

In our virtual Short Course, participants will have a chance to interact with the material and its underlying theory, its applications to diverse social systems, and practical computation. We will pair survey talks on mathematical methods with software tutorials in Python (one on networks and one on topological techniques). To make the software tutorials accessible to those who do not have prior experience with Python, we will provide instructions on downloading software and all relevant toolboxes prior to the Short Course.

Research in complex systems often involves working with data, so we will discuss data ethics and give an overview of different approaches to developing data-driven mathematical models. To help empower participants to communicate across disciplines, we will engage with a panel of multidisciplinary experts on complex social systems. The panelists will share their advice on developing collaborations that span mathematics, political science, sociology, and other fields.

As the first virtual AMS Short Course, our workshop will span three days, with about 4–5 hours of content each day. To be broadly accessible, our course will have a flexible structure, with large tutorials, and (for those who are interested in engaging further) daily discussions in small groups with the organizers and other participants. Our objective is for nonspecialists and early-career researchers to leave the Short Course with new ideas and questions, the foundations for an engaged research and mentoring community, and a springboard for future research in the mathematics and computation of complex social systems.