I discuss a few ideas at the interface of network science and quantum physics. A key idea in this interface is the notion of a quantum walk, which is a generalization of a classical random walk. I will discuss the use of quantum walks to measure the importance (i.e., centrality) of entities in a network and illustrate how local clustering in a network can induce the localization of quantum walks. Finally, I will illustrate how quantum ideas inspire the study of networks with complex-valued weights and advocate that leveraging ideas from mathematical physics has the (insufficiently explored) potential to yield useful insights into network analysis and data analysis.
Speaker: Mason A. Porter is a professor in the Department of Mathematics at UCLA. He also has a secondary appointment in UCLA's Department of Sociology and is an External Professor of the Santa Fe Institute. Mason earned his B.S. in Applied Mathematics at Caltech in 1998 and his Ph.D. from the Center for Applied Mathematics at Cornell University in 2002. After postdoctoral positions at Georgia Tech, Mathematical Sciences Research Institute, and Caltech, Mason joined the faculty in the Mathematical Institute at the University of Oxford in 2007. He moved to UCLA in 2016. Mason studies many topics in complex systems, networks, and nonlinear systems. Thus far, 32 PhD students have completed their doctorates under Mason's mentorship. He has also mentored many postdoctoral scholars and undergraduate students. In 2017, Mason received the Council on Undergraduate Research (CUR) Faculty Mentoring Award (Advanced Career Category) in the Mathematics and Computer Science Division. Mason is a Fellow of the American Mathematical Society, the American Physical Society, the Society for Industrial and Applied Mathematics, and the Network Science Society.
