”Positive Semidefiniteness of Laplacian Matrices of Signed Networks”

Speaker: Ji Liu
Assistant Professor, Stony Brook University

Abstract: This talk will focus on the spectral properties of the Laplacian matrices of undirected weighted graphs with negative weights. Necessary and sufficient conditions for such Laplacian matrices to be positive semidefinite with a simple zero eigenvalue will be presented, which establish relations with effective resistances, multi-port networks, and eventually nonnegative matrices. Their applications in controlling epidemic spreading, stabilizing microgrids, and accelerating distributed computation will also be discussed.

Speaker bio: Ji Liu received the B.S. degree in information engineering from Shanghai Jiao Tong University in 2006 and the Ph.D. degree in electrical engineering from Yale University in 2013. He is currently an Assistant Professor in the Department of Electrical and Computer Engineering at Stony Brook University. He was a Postdoctoral Research Associate at the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, and the School of Electrical, Computer and Energy Engineering, Arizona State University. His current research interests include distributed control and computation, distributed optimization and learning, social and epidemic networks, and cyber-physical systems.