Warren Center Speaker: Chad Giusti

Title: A (very gentle) introduction to algebraic topology for (biological) networks

Abstract: Classical graph-theoretic measures of network structure are focused on local structure: properties of individual nodes, or on paths between them. Statistics derived from these measures thus provide a very node-centric view of the structure of networks. In many applications, however, mesoscale and global features of a system that arise as a result of a low-level network structure are the true subjects of interest. Here, we survey how a new field of “algebraic-topological” tools  for the analysis of network structure is being used to understand these higher-order structures. We will focus on their applications to a wide range of networked biological systems, including evolutionary biology, plant and human circulatory systems, gene regulatory networks, and human and animal neuroscience. No mathematical prerequisites or knowledge of biological systems are assumed.

Bio: Chad Giusti is a Postdoctoral Fellow at the Warren Center for Network and Data Sciences. He studies algebraic, computational, and stochastic topology and their applications, particularly to the study of networks. Recent work involves development of a toolset for detecting the presence of structure (or randomness) in population organization from observations of member activity correlation.