Alex Townsend

About

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I am an Associate Professor in the Department of Mathematics at Cornell University. My research sits broadly in numerical analysis, scientific computing, computational physics, and the theoretical aspects of deep learning.

My current work focuses on spectral methods, low-rank approximation, operator learning, the mathematics of deep learning, and dynamical systems. I am especially interested in problems where rigorous mathematics and effective algorithms sharpen one another.

Background

I received a DPhil in Numerical Analysis from the University of Oxford in July 2014, where I was supervised by Lloyd N. Trefethen. My thesis was titled Computing with functions in two dimensions. Before joining Cornell, I was an Applied Math Instructor at MIT from 2014 to 2016.

Colleagues

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Publications

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Research

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My research combines analysis, algorithms, and computation. Much of it is driven by the question: how can we design methods that are both mathematically principled and genuinely useful for large-scale scientific problems?

Main areas

Spectral methods and numerical analysis

I work on high-accuracy computational methods for differential equations, approximation by functions, and fast transforms. This includes spectral and ultraspherical methods, eigenvalue problems for differential operators, and fast polynomial transforms.

Fast transforms based on asymptotic expansions of special functions

Research talk

Teaching

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Teaching is a central part of my academic work. I care about making advanced mathematics feel coherent, useful, and intellectually alive.

Courses taught at Cornell

MATH 2210: Linear Algebra
MATH 2220: Multivariable Calculus
MATH 2310: Linear Algebra for Data Science
MATH 2930: Differential Equations for Engineers
MATH 2940: Linear Algebra for Engineers
MATH 4250: Numerical Analysis and ODEs
MATH 6220: Applied Functional Analysis
MATH 7270: Top Ten Algorithms of the 20th Century

Earlier teaching

Before Cornell, I was an Applied Math Instructor at MIT from 2014 to 2016.