A picture of me.

Alex Townsend

Associate Professor

Cornell University

townsend@cornell.edu

Malott 589

CV

Current early-career colleagues

Emil Graf
A PhD student in the Mathematics Department at Cornell University. He works on aspects of computational algebraic geometry and we are particularly interested in Moller-Stetter matrices and bivariate analogues of linearizations. We are attempting to make several tools in algebraic geometry more numerically friendly.
Diana Halikias
A PhD student in the Mathematics Department at Cornell University. She works on matrix recovery problems, hierarchical off-diagonal low-rank matrices, and randomized linear algebra. She hopes to apply her knowledge in these topics to tackle some theoretical problems in PDE learning. Before Cornell, she was a mathematics undergraduate at Yale University.
Annan Yu
A PhD student in the Center for Applied Mathematics at Cornell University. He works on classical approximation theory projects such as investigating the stability of perturbed quadrature rules. In addition, he investigates the convergence rates and frequency biasing behavior of neural network training. Before Cornell, he was a mathematics undergraduate at Vanderbilt University.
Christopher Wang
A PhD student in the Department of Mathematics at Cornell University. He works on characterizing hyperbolic PDEs in the context of recovering an underlying solution operator. He also thinks about infinite-dimensional linear algebra for improving data-driven techniques. Before Cornell, he was an undergraduate at Columbia University.
Jennifer Zvonek
A PhD student in the Center for Applied Mathematics at Cornell University. She works on continuous linear algebra and randomized linear algebra. She is particularly interested in computing spectra-related properties of Green's functions and Koopman operators. DMD and Hutchinson's estimates are two algorithms that feature heavily in her work. Before Cornell, she was an engineering undergraduate at UT Austin.

Past postdoc colleagues

Elizabeth Wesson
A postdoctoral student at Cornell in the Center of Applied Mathematics, working with Paul Steen and myself on spectral theories of inertial-capillary motions. In particular, we were developing numerical tools for spherical caps to model droplets resting on surfaces. She is an expert on dynamical systems, queueing theory, and how to wait in traffic (see news article). She is now working in industry in Sommerville, MA.

Past graduate student colleagues

Nicolas Boulle
A DPhil student at the University of Oxford, he works on computing bifurication diagrams and symmetry-exploiting numerical methods for PDEs as well as active fluid simulation in spherical geometries. During the summer of 2017, he was at the University of Oxford working with Patrick Farrell on this topic and at Cornell University for 2017-2018. He is now a postdoc at Cambridge University and soon to be a faculty member in Imperial College London.
Dan Fortunato
He was a graduate student at Harvard in the School of Engineering and Applied Sciences, working on optimal complexity spectral element methods (see paper here), DG methods, and algebraic multigrid. He helped build Wolfram Alpha at Mathematica and worked on multigrid methods at Disney. An expert at both symbolic and numerical computing. He was co-supervised by Chris Rycrott. He is now a research scientist at the Flatiron Institute in New York.
Marc Gilles
He was a graduate student at Cornell in the Center of Applied Mathematics until May 2019, working on continuous analogues of algorithms in linear algebra including the Krylov subspace method for matrices from spectral discretizations of differential equations. Marc was at Facebook working on augumented reality for 18 months. Now, he is a non-tenure-track Assistant Professor at Princeton working with Amit Singer.
Andrew Horning
He was a graduate student at Cornell in the Center of Applied Mathematics, working on the numerical solution of linear and nonlinear differential eigenproblems. He exploited the underlying structure of ultraspherical spectral discretizations to develop faster and more accurate eigensolvers and went on to develop algorithms for computing spectral measures. A mathematician at heart with a strong background in physics. He is currently an Applied Math Instructor at MIT and is soon to become a faculty member at RPI.
Tianyi Shi
He was a graduate student at Cornell University in the Center of Applied Mathematics. He worked on tensor formats, compression algorithms, and computing with tensors that have displacement structure. He was broadly interested in randomized numerical linear algebra, high performance computing, and classical approximation theory. He is now a Research Scientist at LBNL.
Heather Wilber
She was a graduate student at Cornell in the Center of Applied Mathematics. She worked on numerical algorithms for the solution of Sylvester matrix equations with high rank righthand sides (see paper here). She is also the creator of, and main contributor to, Diskfun. She was awarded a NSF graduate fellowship in 2016, a Diversity fellowship in 2016, and a NASA fellowship in 2015. She was an NSF postdoc with Gunnar Martinsson at UT Austin and is now an Assistant Professor at UW in Applied Mathematics.

Past MSc, internships, and undergraduate colleagues

David Darrow
A MIT PRIMES student in 2017 from Hopkins School, working on incorporating the poloidal-toroidal decomposition into numerical solvers of advection-dominated incompressible fluid simulations in polar and spherical geometries. He was co-supervised by Grady Wright from Boise State University. He was an undergraduate student at MIT and is now a PhD student at Princeton.
Jane Du
A MSc student (by research) in Computer Science who completed her undergraduate studies at Cornell University in May 2019. In addition to her MSc courses, she worked on matrix equations, Zolotarev bounds, and data compression algorithms. She had a strong emphasize on randomized linear algebra. She is now a PhD student in computer science at University of Illinois Urbana-Champaign.
Xingrun Ping
An undergraduate student from Shanghai Jiaotong University. In Fall 2019 she did an internship at the Center for Applied Mathematics. She completed two other research internships and worked on learning physical PDE models from experimental simulations, involving both machine learning and high-order PDE solvers. I do not know what she is currently doing.
Sujit Rao
A PhD student at MIT working in both Computer Science and Mathematics. He did research on numerical algorithms for the solution of multivariate polynomial systems with a particular focus on algorithms based on Groebner, border, and H-bases. In 2017 as a Cornell University senior, he achieved a top-200 place in the Putnam exam. He is currently a PhD student at MIT.
Diego Ruiz
A graduate student at the Universidad de Cantabria, Diego did a summer internship at Cornell in 2016. He worked on a new nonuniform fast Fourier transform that is based on low-rank approximation (see paper here). His work allows for fast(er) rotation of functions defined on the sphere, Chebyshev expansion evaluation, and univariate polynomial rootfinding. He is now a math lecturer in Spain.
Aaron Yeiser
A MIT PRIMES student in 2016 from Perkiomen highschool working on a spectral element method for meshes with skinny elements (see resulting paper). His method exploits properties of the ultraspherical spectral method on singularly perturbed differential equations. This research won him a second place at Regeneron STS 2017, worth $175,000 (see Cornell news). He was at MIT as an undergraduate and is now working in industry.