As an undergraduate at UMass, Heather dreamed of integrating mathematics, biology, and medicine. Those same ideas animate her current research. Harrington returns to her alma mater to give a talk, “Comparing computational models and data using computational algebraic geometry and topology” on Thursday, November 1. In anticipation of her visit, we checked in with her about the arc of her research and current projects.
What’s the big idea?
My research is motivated by biological processes. We want to understand how cells make decisions (either to turn genes on or off) or blood vessels to grow towards a tumor. We use mathematical equations called models to study these processes and then compare these mathematical models with data. Rather than perform parameter estimation, we analyze the model by studying the structure of the equations and the shape of the data using recent advances in computational algebraic geometry and topology. These biomedical problems have also motivated new mathematical techniques and are driving new connections between different areas of mathematics.
This is an exciting time to combine algebra, topology and data to solve important problems
Recent advances both theoretically and computationally make analyzing models with real-world state-of-the-art datasets more practical than ever before. This is an exciting time to combine algebra, topology and data to solve important problems that may have consequence to biomedical drug discovery and therapies.
What happens next?
My new EPSRC Grant that started in September (Ulrike Tillmann and I are co-Directors) is titled: "Application-Driven Topological Data Analysis," which falls under the UK "New Approaches to Data Science." We hope to answer the following questions in many different fields:
- Can computational topology serve as a model selection technique for complex data and models, such as those arising in tumor-induced angiogenesis?
- Can we discover new nonporous materials and clusters?
- Can we provide descriptors of dynamical systems data, such as those arising from high dimensional data?
- Can one detect anomalies in large data sets, related to security?
- Can computational topology or other topological invariants provide a way to detect order parameters in topological phases of matter?
We use mathematics to understand processes involved in cancer at the molecular and cellular level. Specifically, our hypothesis of the biological process as well as the experimental data is studied by combining techniques from algebra and computation.
This research is applicable to many areas of science with complex data. We have already studied brain fMRI datasets involved in learning as well as disease (schizophrenia).
Event details for Heather Harrington special Special Colloquium
Video: The shape of data in biology
UK Centre for Topological Data Analysis grant
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