“From the Bridges of Königsberg to Data Analysis” at noon on Thursday 11/21 in Olin 268

Student Colloquium talk by Professor Chris Johnson, Bucknell University

Abstract:  The Prussian city of Königsberg once contained four land masses connected by a series of bridges, and citizens of the city would sometimes ponder the following simple puzzle: is it possible to walk through the city crossing each bridge exactly once?  In analyzing this question, Leonhard Euler noted that the most important feature was how the bridges connected the land masses to one another.  Understanding “connectedness” is one part of a branch of mathematics called topology, and in this talk I will give an overview of a few particular topological ideas.  Beginning with Euler’s nearly 300 year old analysis of the bridges of Königsberg puzzle and ending with some recent developments concerning the shape of a data set, we will see that topological tools can have surprising applications.