The non-alcoholic dollar game drinking game

Algebra Student Seminar
Friday, January 27, 2023 - 10:30am for 1 hour (actually 50 minutes)
Skiles 005
Danial Hwang – Georgia Tech
Trevor Gunn

Chip-firing asks a simple question: Given a group of people and an initial integer distribution of dollars among the people including people in debt, can we redistribute the money so that no one ends up in debt? This simple question with its origins in combinatorics can be reformulated using concepts from graph theory, linear algebra, graph orientation algorithms, and even divisors in Riemann surfaces. This presentation will go over a summary of Part 1 of Divisors and Sandpiles by Scott Corry and David Perkinson. Moreover, we will cover three various approaches to solve this problem: a linear algebra approach with the Laplacian, an algorithmic approach with Dhar's algorithm, and an algebraic geometry approach with a graph-theoretic version of the Riemann-Roch theorem by Baker and Norine. If we have time, we will investigate additional topics from Part 2 and Part 3. As true to the title, there will be a non-alcoholic drinking game involved with this presentation and participation will be completely voluntary. Limited refreshments (leftover Coca-Cola I found in the grad student lounge) and plastic cups will be served.