Sami Davies

Sami Davies
Math Ph.D. Student
University of Washington
Offices: PDL C-404 & CSE2 351
I'm a Ph.D. student at the University of Washington, where I work between the Department of Mathematics and the theory group in the Allen School. I'm fortunate to be advised by Thomas Rothvoss.

Before coming to UW, I earned my B.S. from Carnegie Mellon University and then my M.S. from the University of Illinois at Chicago.


Jan 23

This weekend I’ll be in Nebraska (for the first time) for the Nebraska Conference for Undergraduate Women in Mathematics. I’m happy to be attending this event as an invited graduate student, as several of my friends in grad school benefitted from it as undergraduates!

Jan 12

Heading to Baltimore this week for the AMS short course on Sum of Squares. While I’m in the city, I’ll also be visiting the theory group at Johns Hopkins for a day.

Jun 13

Next week, I’ll be at the Women in Theory Workshop in Boston. Right after, I’m heading to STOC Theory Fest in LA.

Jun 1

I’m continuing to work with FEPPS this summer as an instructor for Math 107, Math in Society. The course samples from a collection of topics like set theory, algebra, finances, and even math history.

Oct 7

Today I start volunteering with FEPPS, the Freedom Education Project for the Puget Sound. I’ll be at the Washinton Corrections Center for Women on Saturday mornings to tutor in study halls for women enrolled in FEPPS’s math courses.

Sep 23

I received the McKibben and Merner Endowed Fellowship in Mathematics for my performance on my preliminary exams and first year courses.

Sep 13

I’m relieved to say that I passed my prelim exams!

Big thanks to my friends in the math department for their collaboration and to my first year professors for their support and availability.

Current Research

Trace Reconstruction

In the trace reconstruction problem, an unknown binary string on n nodes is put through a deletion channel, which deletes each bit with some constant probability, and noisy traces are output. The central question is how many noisy traces are needed to reconstruct the original string with high probability? We study a generalization of the problem on trees. For many classes of trees, including complete trees and spiders, we provide algorithms that reconstruct the labels using only a polynomial number of traces. This exhibits a stark contrast to known results on string trace reconstruction, which require exponentially many traces. Joint work with Miklos Racz and Cyrus Rashtchian.

Santa Claus Problem

Given a set of presents and a set of children who each desire some subset of presents: how should Santa distribute presents among the kids in order to maximize the minimum happiness of any child? We design an approximation algorithm which not only gives a better constant factor approximation than the best known, but which also compares to an LP smaller than those in all previous work. Joint work with Thomas Rothvoss and Yihao Zhang.


A Tale of Santa Claus, Hypergraphs and Matroids
  • Sami Davies
  • Thomas Rothvoss
  • Yihao Zhang
arXiv, July 2018
Algorithms for finding knight's tours on Aztec diamonds
  • Sami Davies
  • Carl Yerger
  • Chenxiao Xue
Involve, a Journal of Mathematics, May 2017

Personal, but work welated


I run a lot. I really like to run. Often it’s with Race Condition Running, which is open to anyone who’d like to join us!

Inclusivity & Engagement
  • Next year, I’ll serve as the secretary for UW’s chapter of AWM. We host events to help create a supportive and inclusive environment for women and underrepresented minorities in mathematics (WUMiM).

  • I teach incarcerated women math through FEPPS.

  • I started volunteering at UW’s Math Circles during the Spring of 2018.