Convergence is the language through which the finite and the infinite converse with each other. This conversation can go both ways: we can understand the infinite by studying the finite (part 1) and the finite by studying the infinite (part 2).<\/p>\n
Part 1: We\u2019ll see a situation where the finite accurately describes the infinite. I\u2019ll introduce a classical model of opinion dynamics that\u2019s difficult to analyze. It turns out this model can be thought of as the limit of a family of models as a certain parameter approaches infinity. We\u2019re able to show that our model captures important dynamics of the \u201cinfinite\u201d model \u2014 for finite parameter values!<\/p>\n
Part 2: We\u2019ll see how dynamics on infinite networks tell us about dynamics on finite networks. Studying large networks of interacting agents can be challenging. A convenient strategy is to use infinitely large networks (the \u201ccontinuum limit\u201d). We do this with functions called graphons which are the limits of sequences of graphs. Under suitable conditions, the solutions of the graphon continuum limit model converge to the solutions of the equivalent models on finite-size networks.<\/p>\n
Do you feel like you have to choose between applied or theoretical math? Between loving graph theory or differential equations? After this talk, I hope you\u2019ll see that with convergence we can bridge the gaps.<\/p>\n","protected":false},"excerpt":{"rendered":"
Convergence is the language through which the finite and the infinite converse with each other. This conversation can go both […]<\/p>\n","protected":false},"author":185,"featured_media":0,"template":"","class_list":["post-5620","event","type-event","status-publish","hentry","event-categories-faculty","event-categories-staff","event-categories-students"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.hmc.edu\/calendar\/wp-json\/wp\/v2\/event\/5620","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hmc.edu\/calendar\/wp-json\/wp\/v2\/event"}],"about":[{"href":"https:\/\/www.hmc.edu\/calendar\/wp-json\/wp\/v2\/types\/event"}],"author":[{"embeddable":true,"href":"https:\/\/www.hmc.edu\/calendar\/wp-json\/wp\/v2\/users\/185"}],"wp:attachment":[{"href":"https:\/\/www.hmc.edu\/calendar\/wp-json\/wp\/v2\/media?parent=5620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}