Speaker: T. Kyle Petersen (DePaul University)
Title: Napkin Problems
Abstract: Suppose a number of mathematicians sit down at a circular banquet table that has napkins evenly spaced between each place setting. When a particular diner sits, they might encounter two napkins (in which case they choose their preferred napkin), they might encounter one napkin because a neighbor already took one (in which case they take the other napkin), or they might encounter zero napkins because both their napkins were already taken by neighbors. If people sit down in a random order and grab napkins from the left or right side of their place at random, what is the expected proportion of napkinless diners? What is the worst order in which people might sit?
In this talk I will tell you the answers to both these questions, as well as some related open questions. Along the way, I will tell you the human story of my engagement with these questions in two different projects with a variety of collaborators, separated by almost 20 years.