Sam Ferguson is a MacCracken Fellow and PhD candidate at the Courant Institute of Mathematical Sciences within NYU. His PhD advisor is Scott Armstrong, and the topic of his dissertation is stochastic homogenization. In particular, it considers an analogue of Hilbert's 19th problem in this context. He enjoys thinking about questions like, "How small can computer chips be made, if manufacturing causes random errors?" which is a natural stochastic homogenization problem.

Before coming to NYU, Sam was a graduate student at the University of Iowa for four years, from 2010 to 2014. In Iowa, he studied solitons in physics, which explain both solitary canal waves and how fiber optics provide high speed internet. In Iowa, he also studied Fuglede's conjecture, which says that a set tiles space exactly when it has a Fourier basis. Counterexamples exist in general, but it is known to be true in various special cases. He has recently returned to this harmonic analysis research.

Sam has also been involved with a variety of outreach activities, encouraging women, students with Asperger's syndrome, and those from socioeconomically underpriveleged groups to pursue the academic interests which most excite them, through activites such as co-organizing Sonia Kovalevsky Day, publishing with the Belin-Blank Center, and giving talks to high school students through Courant Splash.

Sam has taught and tutored students at a variety of levels, from middle school to graduate school, and created a variety of problem-based learning resources for them.

Here are links to Sam's short Curriculum Vitae, long Curriculum Vitae, publication list, an in-class activity from his spring 2018 Discrete Math class at NYU, and a link to the three minute video of him discussing his Obamacare research, made by Time's film crew.

A One-Sentence Line-of-Sight Proof of the Extreme Value Theorem

Link to the paper in the American Mathematical Monthly.

Homogenization, linearization and large-scale regularity for nonlinear elliptic equations, joint with S. Armstrong, T. KuusiLink to the preprint on arXiv.

The Affordable Care Act and the IRS iterative fixed point procedureLink to the preprint on arXiv.

A One-Sentence Inverse Image Proof of Lusin's TheoremFor self-employed people who buy health insurance from a government exchange, IRS guidance for calculating how much money the government should give receive doesn’t always arrive at the right amount. I have written an algorithm, and had a preliminary online calculator created which uses a version of it. Try for yourself!

- Try the Self-Employed ACA calculator Calculator link

- ferguson@cims.nyu.edu
- Office 510, Courant Institute, 251 Mercer Street, 10012, New York, NY
- email for appointment