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UID:0-1785@hmc.edu
DTSTART;TZID=America/Los_Angeles:20260409T161500
DTEND;TZID=America/Los_Angeles:20260409T173000
DTSTAMP:20260402T215038Z
URL:https://www.hmc.edu/calendar/events/mathematical-connections-seminar-t
 he-finite-and-the-infinite-heather-brooks/
SUMMARY:Mathematical Connections Seminar: “The Finite and the Infinite\,
 ” Heather Brooks
DESCRIPTION:Convergence is the language through which the finite and the in
 finite converse with each other. This conversation can go both ways: we ca
 n understand the infinite by studying the finite (part 1) and the finite b
 y studying the infinite (part 2).\n\nPart 1: We’ll see a situation where
  the finite accurately describes the infinite. I’ll introduce a classica
 l model of opinion dynamics that’s difficult to analyze. It turns out th
 is model can be thought of as the limit of a family of models as a certain
  parameter approaches infinity. We’re able to show that our model captur
 es important dynamics of the “infinite” model — for finite parameter
  values!\n\nPart 2: We’ll 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 larg
 e networks (the “continuum limit”). We do this with functions called g
 raphons which are the limits of sequences of graphs. Under suitable condit
 ions\, the solutions of the graphon continuum limit model converge to the 
 solutions of the equivalent models on finite-size networks.\n\nDo you feel
  like you have to choose between applied or theoretical math? Between lovi
 ng graph theory or differential equations? After this talk\, I hope you’
 ll see that with convergence we can bridge the gaps.
CATEGORIES:Faculty,Staff,Students
LOCATION:Shanahan Center\, 320 E. Foothill Blvd.\, Claremont\, CA\, 91711\,
  United States
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