고려대학교 수학과

[20201030 : Colloquium]

1. 일시 : 2020년 10월 30일 (금) 16:30-17:30

2. 장소 : Zoom을 이용한 실시간 온라인 강연

            - 문의 : 김상집 교수(sk23@korea.ac.kr)

3. 연사 : 이강주 박사 (서울대)

4. 제목 : Hodge Laplacians and Simplicial Networks

5. 초록 : 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.