Departmental Colloquium

Date: March 26, 2024

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Persi Diaconis, Stanford University

Title: Adding numbers and shuffling cards

Abstract: When numbers are added in the usual way, 'carries' occur. Carries make a mess and it's natural to ask 'how do the carries go?' How many carries are typical and, if you just had a carry, is it more or less likely that there is a following carry? Surprisingly, the carries form a Markov chain with an 'amazing' transition matrix (are any matrices amazing?). This same matrix occurs in the analysis of the usual way of riffle shuffling cards. I will explain the 'seven shuffles theorem' and the connection. The same matrix occurs in taking sections of generating functions and in understanding the Veronese embedding. I'll try to explain all of this 'in English'.