**Alex Townsend, Department of Mathematics, Cornell University**

*The art and science of low-rank techniques*

Matrices and tensors that appear in computational mathematics are so often well-approximated by low-rank objects. Since random ("average") matrices are almost surely of full rank, mathematics needs to explain the abundance of low-rank structures. We will give various methodologies that allow one to begin to understand the prevalence of compressible matrices and tensors and we hope to reveal underlying links between disparate applications. We will also show how the appearance of low-rank structures can be used in function approximation, fast transforms, and partial differential equation (PDE) learning.

**Bio: **Alex Townsend is an Associate Professor at Cornell University in the Mathematics Department. His research is in Applied Mathematics and focuses on spectral methods, low-rank techniques, fast transforms, and theoretical aspects of deep learning. Prior to Cornell, he was an Applied Math instructor at MIT (2014-2016) and a DPhil student at the University of Oxford (2010-2014). He was awarded a Simons Fellowship in 2022, an NSF CAREER in 2021, a SIGEST paper award in 2019, the SIAG/LA Early Career Prize in applicable linear algebra in 2018, and the Leslie Fox Prize in 2015.