Chip-firing Games on Graphs by Prof. Ralph Morrison, Mathematics Colloquium, Wednesday, June 23, 1 – 2:00 pm, North Science Building B11 (Auditorium)
Abstract: A graph is a collection of nodes connected by edges. We can place a collection of “chips” on the vertices of the graph, and move them around the graph according to certain “chip-firing” moves. There are lots of questions we can then ask: when do two chip placements differ by a sequence of chip-firing moves? When can all “debt” (that is, negative numbers of chips) be eliminated by chip-firing? And how can we find chip placements that can eliminate added debt, no matter where it’s placed? In this talk we’ll answer all these questions and point to lots of open problems; this will include work by SMALL 2018, SMALL 2020, and SMALL 2021.