Prof. Yilun Shang
Prof. Yilun Shang
Northumbria University, UK
Title: Recent advances on variants of Estrada index of random graphs
Suppose that G is a graph over n vertices. G has n eigenvalues of adjacency matrix represented by λ_1, λ_2,..., λ_n. The Estrada index of G is defined as the sum of exp(λ_i) for all i=1,...,n. This graph invariant appeared for the first time in year 2000, dealing with the folding of protein molecules. Since then a variety of other chemical and non-chemical applications of Estrada index and its variants were communicated. In particular, network robustness has found to be a key area that Estrada indices play an important role. In this talk, we will discuss the combinatorial properties of variants of Estrada index of random graphs, including Laplacian Estrada index, Distance Estrada index, and Gaussian Estrada index with a view to their applications in network robustness. 
Dr. Shang received B.S. and Ph.D. degrees in mathematics from Shanghai Jiao Tong University in 2005 and 2010, respectively. His research interests include the structure and dynamics of complex networks and systems, cyber epidemic spreading, probabilistic combinatorics, and system control theory. Prior to joining Northumbria University as an associate professor, he held various appointments with Tongji University, University of Texas at San Antonio, Singapore University of Technology and Design, Hebrew University of Jerusalem, and University of Essex. Dr. Shang is on the Editorial Board of KSII Transactions on Internet and Information Systems, IEEE Access, and Scientific Reports. He received the 2016 Dimitrie Pompeiu Prize from the Romanian Academy.