Current Research Projects
Geometric Complexes
What geometric structures are useful to model a collection of data points? What are their properties? Natural candidates are Voronoi tessellations, Delaunay mosaics and their higher order generalisations. Together with colleagues at ISTA, we try to make sense of these objects through the lenses of discrete Morse theory and persistent homology.
Topology and Data Structures
The persistent homology (PH) of a function encodes topological features of a space at different spatial resolutions. If the function or the space undergo a local change can we update the PH efficiently or shall we just recompute it from scratch? Addressing this question boils down to finding a data structure that efficiently maintains the persistent pairs. I study this question for functions defined on graphs.
Spatial Biology
The tumour immune microenvironment (TME), which showcases the battlefield between the cancer cells and the immune cells, carries important clinical information and varies significantly from patient to patient. Together with colleagues at ISTA, I am developing a geometric and topological language to model the spatial arrangement of cells in the TME as well as a framework to describe their interactions.