Sam Zhang's Homepage

I am a 5th year PhD candidate in applied mathematics at the University of Colorado at Boulder, supported by an NSF Graduate Research Fellowship.

My research applies a wide range of techniques from data science — from statistics and mathematical modeling to surveys and experimentation — toward the study of complex social systems, ranging from academic careers to human rights. My advisor is Aaron Clauset.

During my PhD, I was a (2x) research intern with the MSR NYC Computational Social Science group and a Data Science & Human Rights Fellow with HRDAG. Previously, I worked as a software consultant at Pivotal Labs, a software engineer at multiple startups including on a DARPA project, and as a Data Science for Social Good Fellow at the University of Chicago.

I am organizing to improve public higher education with my labor union, United Campus Workers Colorado, and currently serving my second term on the Executive Board of CWA 7799.

my email is shimian dot my last name at

More about me here.

Pronouns: he/him.
Link to CV
Google Scholar
Github - Mastodon - twitter
Selected Publications
For full publications, see [CV] or [Google Scholar].
  1. S. Zhang, N. LaBerge, S.F. Way, D.B. Larremore, & A. Clauset. Submitted (2023).
  2. S. Zhang, K.H. Wapman, D.B. Larremore, & A. Clauset. Science Advances (2022).
  3. K.H. Wapman, S. Zhang, A. Clauset, & D.B. Larremore. Nature (2022).
I was drawn to study math because I found it to be beautiful. I hope I can share some of that beauty through these interactive visualizations. I made many of these visualizations to learn the concepts myself, but occasionally they are also part of larger projects. Note: many of these visualizations only work on desktop.
An illusion of predictability in scientific results
Even experts think / that well-estimated means / are certain outcomes. (Haiku summary due to MSR poets Dan and Jake). Click the thumbnail for a mini-explainer.
An illusion of predictability in scientific results
Sam Zhang, Patrick R Heck, Michelle Meyer, Christopher F Chabris, Daniel G Goldstein, Jake M Hofman     PNAS, 2023 [paper]
Elliptic curves and traveling wave solutions to the KdV equations
View traveling wave solutions to the KdV equations associated with (points of) elliptic curves.
Ridge unfolding polytopes
Unfold 4-dimensional polytopes using their spanning trees.
Visualizing and unfolding nets of 4-polytopes
Satyan L Devadoss, Matthew S Harvey, Sam Zhang     SoCG, 2022 [paper]
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]
Optimizing prevalence estimates for a novel pathogen by reducing uncertainty in test characteristics
Daniel B Larremore, Bailey K Fosdick, Sam Zhang, Yonatan H Grad     Epidemics, 2022 [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 classical 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
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
The Online Encyclopedia of Integer Sequences (OEIS) from a 10,000 foot view.
A visualization of a geometric bound on convex hulls
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
Using the geometry of language to help permit-seekers find the right municipal land use codes.

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