Chip-firing and algebraic combinatorics

author: Caroline Klivans, Brown University
published: July 19, 2019,   recorded: July 2019,   views: 206


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Chip-firing processes are discrete dynamical systems. A commodity (chips, sand, dollars) is exchanged between sites of a network according to simple local rules. Although governed by local rules, the long-term global behavior of the system reveals unexpected properties, including intricate fractal-like patterns. Early results related chip-firing to classic combinatorial objects such as spanning trees, parking functions, and matroids. In recent years, chip-firing has seen much activity in new directions. Connections have been made, for example, between chip-firing and Coxeter groups, binomial ideals, and Riemann surfaces. In this talk, I will give a broad survey of the theory of chip-firing and its many ties to algebraic combinatorics.

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