Sam Zhang's Homepage

I am a PhD candidate and NSF Graduate Research Fellow in the Department of Applied Mathematics at the University of Colorado at Boulder, and a Data Science and Human Rights Fellow with the Human Rights Data Analysis Group. For the last two summers, I was a research intern with the Computational Social Science group at Microsoft Research NYC. My advisor is Aaron Clauset.

My research is highly interdisciplinary, where I combine mathematics with my experience as a software engineer to study important issues facing society. 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.
Link to CV
Google Scholar
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Recent news
  1. Wapman, K. H., S. Zhang, Clauset, A., & Larremore, D. B. Quantifying hierarchy and dynamics in U.S. faculty hiring and retention. Nature (2022) (Paper at 10.1038/s41586-022-05222-x).
  2. Li, W., S. Zhang, Zheng, Z., Cranmer, S. J., & Clauset, A. Untangling the network effects of productivity and prominence among scientists. Nature Communications 13 (2022), 4907 (Paper at 10.1038/s41467-022-32604-6).
  3. Devadoss, S. L., Harvey, M. S., & S. Zhang. (2022). Visualizing and Unfolding Nets of 4-Polytopes. 38th International Symposium on Computational Geometry (SoCG 2022). (Paper at 10.4230/LIPIcs.SoCG.2022.67).
  4. Larremore, D. B., Fosdick, B. K., S. Zhang, & Grad, Y. H. Optimizing prevalence estimates for a novel pathogen by reducing uncertainty in test characteristics. Epidemics (2022). (Paper at 10.1016/j.epidem.2022.100634).
  5. Larremore, D. B., Fosdick, B. K., Bubar, K. M., S. Zhang, Kissler, S. M., Metcalf, C. J. E., Buckee, C. O., & Grad, Y. H. (2021). Estimating SARS-CoV-2 seroprevalence and epidemiological parameters with uncertainty from serological surveys. eLife, 10, e64206. (Paper at eLife.64206).
  6. LaBerge, N., Wapman, K. H., Morgan, A. C., S. Zhang, Larremore, D. B., & Clauset, A. Subfield prestige and gender inequality in computing. To appear, Communications of the ACM (2022). (Preprint at arXiv:2201.00254).
  7. Bhagat-Conway, M. W. & S. Zhang. Rush-hour-and-a-half: traffic is spreading out post-lockdown. Submitted (2022). (Preprint at OSF:6khsj).
  8. S. Zhang, Heck, P. R., Myers, M. N., Chabris, C. F., Goldstein, D. G., & Hofman, J. M. An illusion of predictibility in scientific results. Submitted (2022). (Preprint at SocArXiv:5tcgs).
  9. S. Zhang, Wapman, K. H., Larremore, D. B., & Clauset, A. Labor advantages drive the greater productivity of faculty at elite universities. Submitted (2022). (Preprint at arXiv:2204.05989).
  10. Benzeev, R., S. Zhang, Rauber, M. R., Vance, E. A., & Newton, P. Formalizing tenure of Indigenous lands improved forest outcomes in the Atlantic Forest of Brazil. Submitted (2022).
  11. Spoon, K., LaBerge, N., Wapman, K. H., S. Zhang, Morgan, A. C., Galesic, M., Larremore, D. B., & Clauset, A. Gender and retention patterns among U.S. faculty. Submitted (2022).
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     socRxiv, 2022 [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]
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 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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