• 장소 : 27동 116호 (zoom 비대면 심사, 회의 ID: 507-199-4835) In this thesis, we investigate the relation between the harmonic cycles of a two dimensional complex and the critical group of its underlying graph. The harmonic space of a cell complex is defined to be the kernel of the combinatorial Laplacian and is naturally isomorphic to the homology group by combinatorial Hodge theory. The critical group of a graph is a finite abelian group which is related to the chip-firing game and has the cardinality equal to the number of spanning trees. For two-dimensional cell complexes obtained by adding an additional edge to an acyclization of a graph, Kim and Kook found a combinatorial formula for the generator of one-dimensional harmonic space over real coefficients, using spanning trees of the given graph. We introduce the refined version of the formula for an integral generator, by tracking the trace of a chip in the action of the critical group on spanning trees.