Problems from the Aim Chip-firing Workshop

These problems come from the “Generalizations of chip-firing and the critical group” workshop held from July 8th–12th, 2013 at the American Institute of Mathematics in Palo Alto, California. A reading list for the workshop included the papers [7], [11], [19], [21], [28], and [30], as well as David Perkinson’s website devoted to sandpiles [29]. The problem session was moderated by Vic Reiner. These notes were recorded by Sam Hopkins. Quotations below are not direct; they are meant to summarize each speaker’s key point (and are certainly subject to my not understanding this point or the mathematics behind it). The problems presented, and comments made about these problems, were as follows: