Geometry and Topology Seminar

The shape of things to come: Topological Data Analysis and biology, from molecules to organisms

Shape is data and data is shape. Biologists are accustomed to thinking about how the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. Less often do we consider that data itself has shape and structure, or that it is possible to measure the shape of data and analyze it. Here, we review applications of Topological Data Analysis (TDA) to biology in a way accessible to biologists and applied mathematicians alike.

The Euler Characteristic Transform, or how a topologist and a plant biologist meet for a beer

Shape is foundational to biology. Observing and documenting shape has fueled biological understanding as the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. The vision of Topological Data Analysis (TDA), that data is shape and shape is data, will be relevant as biology transitions into a data-driven era where meaningful interpretation of large data sets is a limiting factor.

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