Spatially resolved transcriptomics and multiomics measure the gene expression and other modalities across thousands of spatial locations, enabling the characterization and interpretation of spatial patterns. However, the data is measured with error and sparsity. Incorporating the spatial information leads to more meaningful identification of spatial domains. Particularly, tissues form various geometries: cortex and skin are formed into layers, tumors usually form circular blobs, liver lobules are formed into hexagons, etc. We aim to develop rigorous mathematical models of the tissue geometries and the spatial gradients of multiomic status to unveil unknown tissue domains and key genes and multiomic features underlying the spatial organization.

Besides the widely analyzed expression of genes across single cells and in space, the transcribed sequences of genes also undergone variations, either from large-scale mutations (e.g. gene fusions) or from alternative splicing mechanisms. Some gene fusions are identified as cancer drivers and help cancer subtype identification, some alternative splicing isoforms are found to be enriched in diseases. However, the functional influence of most of the sequence variants is still to be discovered. We aim to develop accurate computational tools to identify, quantify, and analyze the sequence variants of gene expression using the advanced technologies.