Geometrical and Topological Data Analysis
In geometric data analysis, we have adapted ideas from quasi-conformal and Teichmuller maps (from complex analysis) and statistics to study wing shapes in insects, recognizing that this framework reflects aspects of the biophysical development of shape in 2-dimensions. We have also applied ideas from projective geometry to study avian egg shape across species, and then deployed a mechanical perspective to quantify the observed variation – thus linking the low-dimensionality of descriptive approaches to the low-dimensionality of predictive approaches. And we have used conformal maps to understand the variability in folding patterns in developing brains, along with physical approaches to explain the patterns mechanistically.
In topological data analysis, we played with the idea of Generalized Erdos Numbers to consider the closeness of nodes in a network, and based on this, thought of a simple clustering algorithm to detect communities of friends. And we are in the process of adapting ideas from homology theory to study the pigmentation patterns in avian eggs with the aim of understanding the psychophysical aspects of pattern recognition among brood parasites.