Hi. I'm Hannah Cairns.
I'm a postdoc at McGill University. I have a PhD in mathematics from Cornell University, where I worked on connections between probability theory and analysis. I'm also into algorithms.
Here is my CV, and
here is my page at Cornell.
My LinkedIn page is
here.
My email is hannah dot abigail dot cairns at the domain gmail dot com.
I'm looking for a postdoctoral position
or job in industry, ideally a job as a programmer or researcher.
Papers and preprints:
The smash sum is the unique sum of open sets satisfying a natural list of axioms. To appear in the Journal d'Analyse Mathematique.
arXiv link. 224 KB PDF.
A proof that the Diaconis-Fulton smash sum of open sets is the only one that satisfies
a short list of natural axioms. It comes with an expository note that shows the existence and
uniqueness of quadrature sets for a large class of positive weight functions:
295 KB PDF.
[Draft] The critical sleep rate for activated random walk on the cycle with one chip per vertex:
240 KB PDF.
Activated random walk is a process with chips on a graph which move around and wake each other up, and fall asleep at a rate. In the extreme case where the walk starts with one chip on every vertex of a cycle, there is a sharp boundary between fast and slow sleep.
Perron's Theorem in an Hour.
Hipster random walks.
Some halting problems for abelian sandpiles are undecidable in dimension three.
This is my improvement and simplification of the
Ramachandran-Schild algorithm for stabilizing sandpiles
on trees. It introduces the concept of "round sequences."
Programming projects:
I have a couple github pages.
cairnsh tends to have more mathematical programs, while...
colaprograms has
less serious programs, like an AR game and an informative kiosk.
Most of the programs are written in Python.
The AR game is written in Unity with C#.
Some other things:
I wrote a single-page app,
Solidplotter, for visualizing
three-dimensional shapes defined by equations. It's designed to be usable on a phone.
I participated in a team at the 2019 AI4Good hackathon at Mila. We wrote a
system for parsing handwritten strings of digits
, for Charitable Analytics International's challenge that asked teams to improve their Meza product.
Our team's program came in second out of five in its category, with 85% accuracy.
Here
is my later version that works a little better, with 92% accuracy.
koreader
is an open-source ebook reader written in Lua, which can be used
on e-ink readers like Kindles or Kobos in place of the stock software.
I contributed by submitting a
patch
that made the touchscreen on the Kobo Aura H
2O work.
This took a little bit of reverse engineering:
I had to figure out how the touch event protocol had changed.
I made a portable wide-band radio scanner which can be used from a cellphone,
using a Raspberry Pi Zero W and an RTL-2832 TV tuner dongle.
The Pi Zero W runs a wifi access point, a simple web server,
and a separate backend server that runs the dongle.
The user carries this all around in a box, and uses it by connecting
their cellphone to the Zero's access point and opening the web page
provided by the server. They can command the scanner to look at
different 10-MHz bands between 24 and 1766 MHz, and see the power
at each frequency at 2 KHz resolution. The backend and web server
are written in Python, using scipy to do the computations, and
the web page uses ajax and jQuery.
Translation:
The Ticket, 2015. Translation of Edogawa Ranpo's story
一枚の切符 (Ichimai no Kippu), 1923.
79 KB PDF.
This is a translation into English of the second published story of
Edogawa Ranpo, an influential mystery writer who worked from 1923 to 1960. To my knowledge it is the first translation of this story. It was done in a couple weeks for a translation competition at Cornell, and, not so surprisingly, it didn't win.