Research
Computational Mathematics
My work ranges from classical spectral methods and randomized linear algebra to operator learning, neural-network approximation, and questions inspired by physics and dynamical systems.
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Applied Mathematics at Cornell
Alex Townsend
I work in numerical analysis, scientific computing, deep learning, and dynamical systems, with a particular interest in spectral methods, low-rank approximation, and operator learning.
Publications
Papers
A compact list of representative work, along with direct links to my full publication record and CV.
View publicationsTeaching
Courses
I’ve taught undergraduate and graduate courses across Cornell’s applied and computational mathematics curriculum.
See teachingCurrent Themes
Research directions
Spectral methods
Algorithms for differential equations, approximation by functions, and high-accuracy scientific computing.
Low-rank
Randomized algorithms, matrix recovery, tensor methods, and the geometry of large data matrices.
Operator learning
Mathematical foundations for learning PDE solution operators, Green’s functions, and related models.
Dynamical systems
Questions about synchronization, Koopman operators, and nonlinear phenomena motivated by real systems.
For students
Prospective graduate students and collaborators
If you are interested in numerical analysis, scientific computing, or mathematically grounded machine learning, the best starting point is the research page and recent publications.