Chip-Firing and Critical Groups of Simplicial Complexes by Emily Lindheim-Marx 23

Chip-Firing and Critical Groups of Simplicial Complexes by Emily Lindheim-Marx 23, Mathematics Senior Thesis Defense, Tuesday, May 16, 1:45 – 2:30 pm, North Science Building 113, Wachenheim.

Abstract:  The critical group is powerful graph invariant in the form of a finite group whose order is the number of spanning trees of the graph.  The chip-firing game is a combinatorial game played on a graph whose gameplay yields the structure of the critical group. Recently, the definitions of chip-firing and critical groups have been extended to the higher critical groups of a simplicial complex.  Similarly, the orders of these contain information about the number of higher-dimensional spanning trees. In this thesis defense, I discuss these higher critical groups in mostly low-dimensional cases, with a special focus on the change in the critical group under the topological operation of suspension.