Mathematics of Discrete Systems

My interest is in developing new mathematical concepts that permit to understand the organization and function of complex networks. I combine techniques and tools from Graph Theory, Linear Algebra, Dynamical systems, Analysis and Statistical Mechanics to characterize the structural and dynamical properties of networks, and their extension to hypernetworks, multiplexes, simplicial complexes and metaplexes. In particular, I am interested in the use of matrix functions, operator theory, geometric embedding, and algebraic topology, among others to characterize properties such as expansibility, topological and functional bottlenecks, organization of clusters, global communicability, “clumpiness”, returnability, embedding into Euclidean spaces, random rectangular graphs, vertex similarity analysis, graph automorphism problems, etc.