Sam Zhang's Homepage

I am a PhD student and NSF Graduate Research Fellow in the Department of Applied Mathematics at the University of Colorado at Boulder. My advisor is Aaron Clauset.

My research is in computational social science and applied and interdisciplinary statistics more broadly. I also love making mathematical visualizations, many of which are on display below.

Let's collaborate! Send me an email at:
my email is shimian dot my last name at

More about me here.

Pronouns: he/him.
Ridge unfolding polytopes
Unfold 4-dimensional polytopes using their spanning trees. Joint work with Matt Harvey and Satyan Devadoss.
Bayesian inference for COVID-19 testing
My brief foray into epidemiology at the start of COVID-19. Bayesian methods and interactive tools for informing COVID-19 surveillance testing strategies.
Estimating SARS-CoV-2 seroprevalence and epidemiological parameters with uncertainty from serological surveys
Daniel B Larremore, Bailey K Fosdick, Kate M Bubar, Sam Zhang, Stephen M Kissler, C Jessica E Metcalf, Caroline O Buckee, Yonatan H Grad     eLife, 2021 [paper]
Jointly modeling prevalence, sensitivity and specificity for optimal sample allocation
Daniel B Larremore, Bailey K Fosdick, Sam Zhang, Yonatan H Grad     bioRxiv, 2020 [paper]
Curve shortening
Deform a curve with a discrete curve shortening flow.
A catastrophe machine
Move the center of gravity of a wedge balancing on a table, and observe its corresponding catastrophe surface.
Linear regression, the old fashioned way
Perform ordinary least squares through a set of points with nails, springs, sleeves, and a frictionless rod.
A moduli space for triangles
A solution to a problem by Lewis Carroll using a clever moduli space. For fun, pick points on the moduli space, and watch triangles deform between them along geodesics.
The cross-section of a cylinder is an ellipse
A classic proof that the cross-section of a cylinder is an ellipse. I have no idea why, but this is the most popular blog post on my website.
Whitney's Umbrella
First steps in visualizing 3d mathematics using javascript. A famous surface with a cuspidal point.
Voronoizer bookmarklet
Draw a Voronoi diagram over any webpage with this bookmarklet.
Voronoize this page!
This page has a Voronoi diagram drawn over it, with link and input HTML elements as points.
Treasure hunting
You have been given flawed instructions for finding treasure on an island, but geometry may be able to help.
An ascii implicit function plotter
Plot an elliptic curve (or any implicit function) using ASCII art!
What happens if you rotate a smaller circle inside of a larger circle?
Cats on ladders
Test your geometric intuition with the following problem. A cat is sitting on a ladder leaning against the wall, and the ladder slips. What shape does the cat draw through the air?
A network look at integer sequences
View the Online Encyclopedia of Integer Sequences (OEIS) from a 10,000 foot view.
A visualization of a geometric bound on convex hulls
Interact with a lemma that bounds the size of a convex hull of points based off circles centered at those points.
Building a municipal land use code search engine using a graph of word embeddings
A technical blog post about a successful approach using the geometry of language to help permit-seekers search through municipal land use codes.

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