Escapades in Burn-off Chip-firing on Graphs

Document Type

Presentation Abstract

Presentation Date

9-19-2016

Abstract

Start by placing piles of indistinguishable chips on the vertices of a graph. A vertex can fire if it's supercritical; i.e., if its chip count exceeds its valency. When this happens, it sends one chip to each neighbour and annihilates one chip. Initialize a game by firing all possible vertices until no supercriticals remain. Then drop chips one-by-one on randomly selected vertices, at each step firing any supercritical ones. Perhaps surprisingly, this seemingly haphazard process admits analysis. And besides having diverse applications (e.g., in modelling avalanches, earthquakes, traffic jams, and brain activity), chip firing reaches into numerous mathematical crevices. The latter include–alphabetically–algebraic combinatorics, discrepancy theory, enumeration, graph theory, stochastic processes, and the list could go on (to zonotopes(!)). I'll share some joint (old and new) work–with my colleague and former PhD student Dave Perkins–that touches on a few items from this list. The talk'll be accessible to non-specialists. Promise!

Additional Details

Monday, September 19, 2016 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

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