A picture of me.

Alex Townsend

Assistant Professor

Cornell University

townsend@cornell.edu

Malott 589

CV


Current early-career 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 2017, he was at the University of Oxford working with Patrick Farrell on this topic. He is now an intern at Cornell University for 2017-2018.
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 will be working on matrix equations, Zolotarev bounds, and data compression algorithms. She will have a strong emphasize on randomized linear algebra.
Dan Fortunato
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 is co-supervised by Chris Rycrott.
Andrew Horning
A graduate student at Cornell in the Center of Applied Mathematics, working on the numerical solution of linear and nonlinear differential eigenproblems. He is exploiting the underlying structure of ultraspherical spectral discretizations to develop faster and more accurate eigensolvers. A mathematician at heart with a strong background in physics.
Xingrun Ping
An undergraduate student from Shanghai Jiaotong University who is doing a Fall 2019 internship at the Center for Applied Mathematics. She already has completed two other research internships and will be working on learning physical PDE models from experimental simulations, involving both machine learning and high-order PDE solvers.
Tianyi Shi
A second-year graduate student at Cornell University in the Center of Applied Mathematics. He works on tensor formats, compression algorithms, and computing with tensors that have displacement structure. He is broadly interested in randomized numerical linear algebra, complex analysis, and classical approximation theory.
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 are 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).
Heather Wilber
A graduate student at Cornell in the Center of Applied Mathematics. She works 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.

Past early-career 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 is currently an undergraduate student at MIT.
Marc Gilles
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 is now at Facebook working on augumented reality.
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.
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 is currently at MIT as an undergraduate.