Explore the application of algebraic topology to single-cell sequencing data in this 45-minute talk from the Applied Algebraic Topology Network. Delve into the interpretation of one-dimensional cohomology classes in hallmark gene subsets as models for transient biological processes. Learn how persistent cohomology is used to identify features and how the integration of differential forms estimates gene cascades associated with underlying gene expression dynamics. Discover how this approach can infer cell-cycle processes and homeostatic negative feedback loops from the structure and geometry of point clouds representing RNA expression levels in cells. Gain insights into cutting-edge techniques for analyzing complex biological data through the lens of advanced mathematical concepts.