Alex Townsend, Department of Mathematics, Cornell University
The art and science of low-rank techniques
Matrices聽and聽tensors that appear in computational mathematics are so often well-approximated by聽low-rank聽objects. Since random ("average")聽matrices聽are almost surely聽of聽full聽rank, mathematics needs to explain聽the聽abundance聽of聽low-rank聽structures. We will give various methodologies that allow one to begin to understand聽the聽prevalence聽of聽compressible聽matrices聽and聽tensors聽and聽we hope to reveal underlying links between disparate applications. We will also show how聽the聽appearance聽of聽low-rank聽structures can be used in function approximation, fast transforms,聽and聽partial differential equation (PDE) learning.
叠颈辞:听Alex聽Townsend聽is聽an Associate聽Professor at Cornell University in聽the聽Mathematics Department. His research is in Applied Mathematics聽and聽focuses on spectral methods,聽low-rank聽techniques, fast transforms,聽and聽theoretical aspects聽of聽deep learning. Prior to Cornell, he was an Applied Math instructor at MIT (2014-2016)聽and聽a DPhil student at聽the聽University聽of聽Oxford (2010-2014). He was awarded a Simons Fellowship in 2022, an NSF CAREER in 2021, a SIGEST paper award in 2019,聽the聽SIAG/LA Early Career Prize in applicable linear algebra in 2018,聽and聽the聽Leslie Fox Prize in 2015.