Infinite Simplices: An Excursion into Simplicial Sets


Slides here. This was a public talk, open to members of the Honors, Scholars and Fellows Society of Florida State University

Abstract: The first use of a graph of a network can be traced back to Euler on his solution to the Bridges of Konigsberg problem. Since then, graphs have been mainly a mathematical curiosity. The acceptance of graphs by the wider scientific community has exploded in the past twenty years or so, especially after the very humbling and exciting endeavor of mapping of the network of the code of our origins a.k.a., the Human Genome Project. However, many of the common utilizations of graphs rely on a finite amount of data, however large. In this talk, we'll introduce the notion of a simplicial set, which generalizes the notion of a graph to account for an infinite amount of data. Time permitting, we'll look into an example of these infinite graphs applied to the modelling of misinformation.