Opinion Dynamics on Sheaves - AMSS-YMSC-BIMSA Joint Seminar on Progress of Topology and Its Applications

Opinion Dynamics on Sheaves

Organizers

Haibao Duan , Fei Han , Yong Lin , Jianzhong Pan , Guo-Wei Wei , Jie Wu , Kelin Xia , Shing Toung Yau , Chao Zhou

Speaker

Robert Ghrist

Time

Tuesday, November 29, 2022 9:00 AM - 10:30 AM

Venue

Online

Zoom 787 662 9899 (BIMSA)

Abstract

There is a long history of networked dynamical systems that models the spread of opinions over social networks, with the graph Laplacian playing a lead role. One of the difficulties in modelling opinion dynamics is the presence of polarization: not everyone comes to consensus. This talk will describe work with Jakob Hansen introducing a new model for opinion dynamics using sheaves of vector spaces over social networks. The graph Laplacian is enriched to a Hodge Laplacian, and the resulting dynamics on discourse sheaves can lead to some very interesting and perhaps more realistic outcomes. Extensions of these ideas to sheaves of lattices (in joint work with Hans Riess) will also be surveyed.

Speaker Intro

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.