제목: Hodge Laplacians and simplicial networks
연사: 이강주 박사님 (서울대학교)
일시: 10월 30일 금요일 오후 4시 30분
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Abstract: The Hodge Laplacian on a simplicial complex is a discrete analogue of the Laplace-Beltrami operator. Combinatorial Hodge theory says that the kernel of this operator is isomorphic to the homology group as a vector space, and an element of the space satisfies the energy-minimizing property. Based on the theory, we introduce the notion of effective resistance for simplicial networks. We present a formula for the simplicial effective resistance via high-dimensional tree-numbers, providing its combinatorial interpretation. Moreover, as a tool for analyzing simplicial networks, we suggest a definition of information centrality for simplicial networks.