The Grand Rapids Community College Mathematics Department is pleased to announce that it will host its next Mathematics Seminar on Thursday, December 10, 3:00-4:15 PM in 103 Cook. Our speaker, GRCC student Grant Jenkins, will discuss applications of Graph Theory. The title and abstract of his talk are below.
Grant’s seminar should be of interest to a wide cross-section of the college community. There will be cool mathematics with applications to romance and personal choice - what a combination! Very little background in mathematics is required, and everyone is welcome to attend.
Pop and cookies will be served at 2:45 PM.
The Stable Marriage Problem: An Intersection of Social Choice and Mathematics
The problem: Imagine that we are playing matchmaker. We have 10 male clients and 10 female clients who wish to be matched with someone of the opposite sex. Each of the 20 clients gives us a list of rankings of who they wish to be matched with. How do we use these lists to arrange 10 happy marriages?
This talk will rely on a field of mathematics called graph theory to match together people based upon a list of preferences. We aim to create a “stable marriage” in order to cater to as many individuals’ preferences as possible. This is accomplished with the Gale-Shapely Algorithm, which allows us to identify a definitive set of matchings. In reality, peoples’ rankings of each other - preferences - are not always strict and sometimes include indifferences. In this case, we can extend Gale-Shapely to find matchings. This introduces many new classifications of stability and gives us a glimpse into interactions between social choice and mathematics.