Combinatorics and the geometry of the chip firing game


Ponente: Fatemeh Mohammadi (Institute of Science and Technology, Austria)

Lugar: Seminario Chicho (Aula 314, Edificio Vives)

Hora: viernes 24 de abril, 13:00

La charla forma parte del ciclo de conferencias «Big Data and Biomedical Informatics Week» coordinado por Julio Rubio

Abstract: The chip firing game is a solitaire game on graphs which has a very beautiful and rich mathematical structure, and it appears in several fields of mathematics and statistics. It starts from a configuration of dollars (chips) on the vertices of a fixed graph: in each step of a chip-firing game we may choose a vertex to lend one dollar to each of its neighbours, or to borrow one dollar from each of its neighbours. The goal of the game is to get all the vertices out of debt (with non-negative integers) by a sequence of legal moves. For any finite graph, there are only finitely many critical configurations whose vertices are not in dept and no subset of vertices can fire without going into debt. I will talk about these critical configurations, and some related combinatorial and algebraic objects. The talk will be aimed at a general audience.