Topic: Sketching and subspace embeddings

Michal Dereziński discusses oblivious subspace embeddings, random dimension-reduction maps that approximately preserve all vector norms in a low-dimensional subspace. Such maps support least-squares regression and low-rank approximation, yet efficient optimal embedding dimensions have left a gap between theory and practice. Analyzing universality in sparse random matrices leads to a resolution of the Nelson–Nguyen conjecture up to sub-polylogarithmic factors in SODA 2026. Joint work with Shabarish Chenakkod, Xiaoyu Dong, and Mark Rudelson.

Joel Tropp studies structured dimension reduction through the injectivity of random maps, motivated by fast low-rank approximation and least-squares regression. This viewpoint sharpens guarantees for sparse maps and gives exponential improvements for tensor-product dimension reduction. Experiments assess the resulting structured random matrices on synthetic problems and scientific applications. Joint work with Chris Camaño, Ethan Epperly, and Raphael Meyer, available as arXiv:2508.21189.