Abstract: Social networks play a crucial role in how we share and discuss ideas. This talk delves into the mathematics behind the spread of information (such as opinions or beliefs) on these networks. Imagine a network as a complex web, where each node represents an individual and the connections represent interactions. Opinions, beliefs, arguments, and other social contagions reside in data structures atop this social network, and the dynamics of such information flows don’t always converge to consensus, leading to phenomena like polarization.

The talk will touch on classical and novel approaches to modeling these dynamics using ideas from network theory, differential equations, and algebraic topology.

This talk is a general-level exposition aimed at all who are curious about the intersection of mathematics and social information dynamics. A little bit of exposure to vectors and linear algebra may be useful, but no sophisticated mathematical prerequisites will be assumed.

Robert Ghrist is the Andrea Mitchell PIK Professor of Mathematics and Electrical & Systems Engineering at the University of Pennsylvania. After earning a BS in Mechanical Engineering (University of Toledo, 1991), and the MS and PhD in Applied Mathematics (Cornell University, 1994, 1995), he held positions in Mathematics departments at the University of Texas (Austin), Georgia Tech, and the University of Illinois (Urbana-Champaign). He has been at Penn since 2008. Ghrist is a recognized leader in the field of Applied Algebraic Topology, with publications detailing topological methods for sensor networks, robotics, signal processing, data analysis, optimization, and more. He is the author of a leading textbook on the subject (Elementary Applied Topology, 2014), and has managed numerous large DoD grants from AFOSR, ASDRE, DARPA, and ONR. His research has been recognized with the NSF CAREER, NSF PECASE, SciAm50, and Vannevar Bush Faculty Fellow awards. Ghrist has been an invited speaker at two International Congresses of Mathematicians: once (Madrid 2006) for research and once (Seoul, 2014) for education. Ghrist is a dedicated expositor and communicator of Mathematics, with teaching awards that include the MAA James Crawford Prize, Penn’s Lindback Award, and the S. Reid Warren award in Engineering at Penn. Ghrist is the author, designer, and animator of popular YouTube video texts (featureing the Calculus BLUE Project), as well as an online course on Coursera featured in the New York Times, BoingBoing, and Gizmodo. He currently serves as  the Associate Dean of Undergraduate Education for the School of Engineering and Applied Science at Penn.

A reception preceding the lecture will begin at 5:00 in the SAS Hall atrium.

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