Department of Mathematics colloquium - Sibe Mardešić presents a sequence of lectures given by leading experts in the fields of theoretical and applied mathematics. The lectures take place at the Department of Mathematics, Faculty of Science, Bijenička cesta 30, Zagreb.
About the lecturer: Michele Benzi is full professor of Numerical Analysis at the Scuola Normale Superiore in Pisa. He was previously the Samuel Candler Dobbs Professor of Mathematics and Computer Science at Emory University, which he joined in 2000 after holding positions at the University of Bologna, CERFACS, and Los Alamos National Laboratory. His degrees are from the University of Bologna (1987) and North Carolina State University (1993). His research interests are in numerical linear algebra, with a focus on the solution of large sparse linear systems, especially preconditioning techniques for saddle point problems, and matrix functions. In recent years he has contributed algorithms for the numerical solution of the incompressible Navier-Stokes equations and for the analysis of complex networks. He serves on the editorial board of over 15 journals and he is a Fellow of the Society for Industrial and Applied Mathematics (elected 2012) and a Fellow of the American Mathematical Society (elected 2018). He was elected a member of the Academia Europaea in 2019.
Lecture abstract: Functions of matrices have long been an object of study in matrix theory, starting with the early works by Cayley and Sylvester laying the foundations of linear algebra. It is well known that matrix functions play an important role in the solution of systems of linear differential equations and more generally in many problems of mathematical physics. In recent years, matrix functions have found novel applications in the analysis of complex graphs (or networks), where they can be used to define graph metrics such as node centrality and communicability measures, to quantify the degree of bipartivity, and to study a variety of dynamical processes. Through these problems, matrix functions have found widespread application in the most disparate fields including brain physiology, social network analysis, transportation networks, cell biology, bibliometry, and many others. In this talk I will give a survey on matrix functions, together with some examples of their use in Network Science. The talk is self-contained and requires only a basic knowledge of linear algebra and analysis.