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Alex Townsend, Department of Mathematics, Cornell University

The art and science of low-rank techniques

MatricesÌýandÌýtensors that appear in computational mathematics are so often well-approximated byÌýlow-rankÌýobjects. Since random ("average")ÌýmatricesÌýare almost surelyÌýofÌýfullÌýrank, mathematics needs to explainÌýtheÌýabundanceÌýofÌýlow-rankÌýstructures. We will give various methodologies that allow one to begin to understandÌýtheÌýprevalenceÌýofÌýcompressibleÌýmatricesÌýandÌýtensorsÌýandÌýwe hope to reveal underlying links between disparate applications. We will also show howÌýtheÌýappearanceÌýofÌýlow-rankÌýstructures can be used in function approximation, fast transforms,ÌýandÌýpartial differential equation (PDE) learning.

Bio:ÌýAlexÌýTownsendÌýisÌýan AssociateÌýProfessor at Cornell University inÌýtheÌýMathematics Department. His research is in Applied MathematicsÌýandÌýfocuses on spectral methods,Ìýlow-rankÌýtechniques, fast transforms,ÌýandÌýtheoretical aspectsÌýofÌýdeep learning. Prior to Cornell, he was an Applied Math instructor at MIT (2014-2016)ÌýandÌýa DPhil student atÌýtheÌýUniversityÌýofÌýOxford (2010-2014). He was awarded a Simons Fellowship in 2022, an NSF CAREER in 2021, a SIGEST paper award in 2019,ÌýtheÌýSIAG/LA Early Career Prize in applicable linear algebra in 2018,ÌýandÌýtheÌýLeslie Fox Prize in 2015.