Graphs and Hypergraphs and Topology, Oh My!

Monday October 21 at 4pm in Olin 201. Emily Purvine, of the Pacific Northwest National Lab will talk about how mathematical structures and concepts can be great models of real-world data. For example, differential equations have a long history of success in applied mathematics to model dynamics found in rivers and oceans, the atmosphere, and molecular systems (just to name a few!). Network science is an area of applied math that uses graph structures to model relational systems like social, collaboration, and transportation networks. Graphs, however, are limited to modeling pairwise relationships among entities. Hypergraphs and topological spaces provide alternate models of relational systems that allow for arbitrary sized and structured relationships. In this talk, Dr. Purvine will introduce the mathematical concepts of graphs, hypergraphs, and topology and show how they are used to model real-world data from a variety of applications including biological systems, chemistry measurements, and cyber networks. Dr. Purvine will also talk about what measurements and properties of these structures can tell us about the systems they model.

BIO: Dr. Emilie Purvine is a mathematician and data scientist at Pacific Northwest National Laboratory. She joined PNNL in 2011 after receiving her PhD in mathematics from Rutgers University with a focus on enumerative combinatorics and nonlinear recurrence relations. While at PNNL Emilie has had the opportunity to contribute to a variety of projects tackling hard problems in applications including computational biology and chemistry, power grid modeling, cyber network analysis, and knowledge models. Her current mathematical research focus is on topological data analysis applied to discrete structures like graphs and hypergraphs. Much of her work involves finding mathematical nuggets in applied domains and working on theoretical advances to enable operational progress.

Emilie also greatly values the ability to make mentoring a focus of her work. She loves to give presentations to students at all levels to provide an example of what a mathematician can do outside of academia. Interns and postgraduates (2-3 year temporary employees including post bachelors, post masters, and postdoc) are always included into her projects to promote on the job learning.

Outside of her core work activities Emilie has also been the chair of the MAA’s Membership Committee and an associate editor of the AMS Notices. In her free time Emilie spends time with her friends and family, enjoys a good book, loves the outdoors and traveling to new destinations.