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Explore a mathematical research talk examining the geometric aspects of single-cell RNA sequencing analysis and trajectory inference. Delve into how RNA sequencing quantifies gene expression at individual cell levels, where each cell's expression is represented as a vector containing gene expression levels. Learn about the challenges of reconstructing dynamic cellular processes from destructive sequencing techniques, and discover how RNA velocity vectors help predict future changes in gene expression. Understand the mathematical framework for trajectory inference in cell differentiation, where expression vectors distribute along tree structures, and examine the methods for estimating shortest path distances using metrics on integral curves of RNA velocity fields. This presentation was delivered as part of the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" at the Erwin Schrödinger International Institute for Mathematics and Physics.
