Anna Song

I am currently in my final 4th year of PhD (2019-2023) at the Department of Mathematics of Imperial College London and in the Haematopoietic Stem Cell Laboratory at the Francis Crick Institute, under the joint supervision of Anthea Monod and Dominique Bonnet.

I work at the interface between mathematics and biology, having a keen interest in the connections between abstract ideas and real life phenomena, especially anything related to shapes, colors, and patterns in data. These beautiful connections are sometimes surprisingly relevant, despite their simplicity.

My research fields include mathematical modeling, geometry, topology, and imaging; here, programming is essential to applying abstract models on real data. 

You can have a look at the curvatubes model, which offers a compact geometric description of shapes with patterns, such as vascular networks or porous materials. To quantify such shapes, I propose to use signed distance persistent homology or SDPH, and to generalize Morse theory to distance functions in order to interpret the SDPH persistence diagrams. You can also see here how topological data analysis can help to identify significant cycles and patterns in point cloud data.