Recorded 24 February 2026. Tuca Auffinger of Northwestern University presents "Open Mathematical Problems in Manifold Learning for Single-Cell Data" at IPAM's Mathematics of Cancer: Open Mathematical Problems Workshop. Abstract: Single-cell transcriptomics has revolutionized cancer research, allowing us to characterize intratumoral heterogeneity and continuous developmental trajectories. Dimensionality reduction techniques, specifically t-Distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP), have become the standard for visualizing these high-dimensional manifolds. However, while these algorithms are successfully used as investigative tools, their mathematical foundations regarding global structure preservation, stability, and interpretability remain fragile. In this talk, I will highlight these specific open problems. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/mathematics-of-cancer-open-mathematical-problems/