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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 mo-tivated by public opinion, political elections, social media, and social advocacy. Through a combination of survey lectures, software tutorials, panels, and community-build-ing 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 math-ematical 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 over-view 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 sys-tems. 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

We—Heather Z. Brooks (Harvey Mudd College), Michelle Feng (California Institute of Technology), Mason A. Porter (University of California, Los Angeles), and Alexandria Volkening (Northwestern University)—are delighted to organize the 2021 AMS Short Course.

Our speakers and panelists, who span multiple disci-plines, include Daryl R. DeFord (Washington State Univer-sity), Sandra González-Bailón (University of Pennsylvania), Elizabeth Munch (Michigan State University), Nancy Ro-dríguez (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 mathemat-ical and computational techniques that researchers and

AMS Short CourseMathematical and Computational Methods for Complex Social SystemsCyberspace, January 3–5, 2021

october 2020 Notices of the AmericAN mAthemAticAl society 1475

MEETINGS & CONFERENCES

Python Tutorial on NetworksDaryl R. DeFordDRD is an assistant professor in the Department of Mathematics at Washington State University. In his research, he applies algebraic and combinatorial methods to problems in data analysis, with a special focus on political redistricting and gerry-mandering.

DRD’s software tutorial will build on HZB’s survey lecture on networks, and he will introduce participants to NetworkX, a widely used Python package for developing and analyzing networks.

Topological TechniquesMichelle FengMF is a John S. McDonnell Foun-dation Postdoctoral Fellow in the Department of Computing + Math-ematical Sciences at California Insti-tute of Technology. Her research is on the applications of topological methods to data with strong spa-tial components, including voting patterns, gerrymandering, neighbor-

hood segregation, and city organization.MF will introduce participants to how topological tech-

niques—particularly persistent homology—can be applied to social-systems data to better understand its structure across scales.

Python Tutorial on TDAElizabeth MunchEM is an assistant professor at Mich-igan State University in the Depart-ment of Computational Mathemat-ics, Science, and Engineering and the Department of Mathematics. Her research area is applied topology and topological data analysis (TDA).

EM’s software tutorial, which will follow MF’s introduction to topologi-

cal techniques, will give participants additional exposure to Python and highlight toolboxes that are often used when applying TDA to data from complex systems.

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 research-ers 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.

Reading MaterialsTo learn more about complex social systems, we recom-mend the following resources:

• E. J. Amézquita, M. Y. Quigley, T. Ophelders, E. Munch, and D. H. Chitwood, The shape of things to come: Topolog-ical data analysis and biology, from molecules to organisms, Dev. Dyn. 249 (2020), no. 7, 816–833.

• D. Brockmann, Complexity explorables, available at https://www.complexity-explorables.org.

• F. Bullo, Lectures on Network Systems, Ed. 1.4, with contri-butions by J. Cortés, F. Dorfler, and S. Martinez, Kindle Direct Publishing, 2020, available at motion.me.ucsb .edu/book-lns.

• M. De Domenico et al., Complexity explained, available at https://complexityexplained.github.io, 2019.

• S. González-Bailón, J. Borge-Holthoefer, A. Rivero, and Y. Moreno, The dynamics of protest recruitment through an online network, Scientific Reports 1 (2011), 197.

• E. Horvitz and D. Mulligan, Policy forum. Data, privacy, and the greater good, Science 349 (2015), no. 6245, 253–255.

• D. A. McFarland, J. Moody, D. Diehl, J. A. Smith, and R. J. Thomas, Network ecology and adolescent social structure, Amer. Sociol. Rev. 79 (2014), no. 6, 1–34.

• E. Munch, A User’s Guide to Topological Data Analysis, J. Learning Analytics 4 (2017), no. 2, 47–61.

Lecture TopicsNetworks in Social SystemsHeather Z. BrooksHZB is an assistant professor in the Department of Mathematics at Har-vey Mudd College. She studies com-plex systems with tools from network theory and dynamical systems. Her research is in diverse applications, in-cluding polarization on social media, group and committee diversity, and youth gang reduction programs in LA.

In her survey lecture, which will serve as an introduction to networks for those who are new to the field, HZB will show how different complex social systems can be modeled and analyzed from a network-theory perspective.

Heather Brooks

Daryl R. DeFord

Michelle Feng

Elizabeth Munch

1476 Notices of the AmericAN mAthemAticAl society Volume 67, Number 9

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applications to social, biological, or ecological systems.

SMS is a PhD student in ecol-ogy and evolutionary biology at the University of Tennessee, Knoxville. She develops cellular-automata and statistical models, with a particular focus on better understanding gun violence in Chicago, IL.

JHT is an associate professor of mathematics at The Ohio State Uni-versity. His work spans infectious-dis-ease dynamics, network science, and the application of data-science meth-ods to support civic engagement.

CMT is a professor of mathematics at Williams College and the founder of the Institute for the Quantitative Study of Inclusion, Diversity, and Eq-uity. His research area is data science and dynamical systems, often with applications to social justice.

JNV is an associate professor of political science at George Mason University. Her work focuses on cam-paign finance, election dynamics, social networks, lobbying, and other problems related to U.S. politics.

The field of complex systems is inherently interdisciplinary. In this panel of multidisciplinary experts, the speakers will respond to ques-tions from the Short Course partici-pants, provide advice on developing cross-disciplinary collaborations, and share their experiences with commu-nicating across fields.

RegistrationRegistration will open in September. Please see the AMS Short Course webpage at https://www.ams.org /short-course-general for more information.

CreditsPhotograph of Nancy Rodríguez is courtesy of UNC Chapel

Hill.Photograph of Shelby M. Scott is courtesy of Raphael Rosalin.Photograph of Joseph H. Tien is courtesy of Rebecca Tien

Photography.Photograph of Jennifer N. Victor is courtesy of Julia Victor.

Data EthicsMason A. PorterMAP is a professor in the Depart-ment of Mathematics at UCLA. He is also an affiliated faculty member of UCLA’s Center for Social Statistics.

MAP’s research concerns network analysis, applications of mathematics to social systems, and complex and nonlinear systems. He is a Fellow of the American Mathematical Society,

the American Physical Society, and the Society for Industrial and Applied Mathematics.

Finding and analyzing data that is associated with social systems comes with significant challenges and concerns. In this lecture, MAP will discuss some questions and best practices to keep in mind when working with data.

Data-Driven ModelingAlexandria VolkeningAV is an NSF-Simons Fellow in the NSF-Simons Center for Quantitative Biology and the Department of En-gineering Sciences & Applied Math-ematics at Northwestern University. Her research focuses on complex sys-tems and emergent behavior, and she develops and analyzes models for a range of applications, including pat-

tern formation, election dynamics, and crowd movement.In her overview lecture, AV will introduce participants

to data-driven modeling and highlight some of the differ-ent types of models that are used to describe and analyze complex systems across various applications.

Panel: Collaborating Across DisciplinesSandra González-Bailón, Nancy Ro-dríguez, Shelby M. Scott, Joseph H. Tien, Chad M. Topaz, and Jennifer N. VictorSGB is an associate professor in the Annenberg School for Communica-tion at the University of Pennsylvania. Her research applies computational social-science tools to the analysis of political communication, including social-media activity, information diffusion, political mobilization, and news consumption.

NR is an assistant professor in the Department of Applied Mathemat-ics at the University of Colorado, Boulder. Her research is in partial differential equations, often with

Mason A. Porter

Alexandria Volkening

Nancy Rodríguez

Sandra González- Bailón

Shelby M. Scott

Joseph H. Tien

Chad M. Topaz

Jennifer N. Victor