About
I’m a 5th year PhD student at the University of British Columbia supervised by Young-Heon Kim.
Website is currently in flux
I’m currently (2024/11/18) in the middle of upgrading this website and its contents, since I haven’t done so since undergrad. Thus there will be some weird things happening for the next few weeks where some information is redundant between pages, some information is outdated, some things from undergrad that should have been removed (but haven’t yet) remain floating around, etc.
If you notice weird compile errors / broken links in any of the documents/pages, please send me an email (\(\newcommand{\tryandscrapethisnowhahaha}{\hspace{-.2em}\Huge\text{.}}\text{fk}\phantom{abcd}\hspace{-1.9em}\text{ob}\phantom{hehe}\hspace{-2.1em}\text{ayashi}@\text{hm}{\rm c}_{\hspace{-.5em}\phantom{a}^{\hspace{-.35em}\phantom{a}_{\tryandscrapethisnowhahaha}}}\hspace{-.2em}\text{edu}\)). In light of the Kafkaesque nightmare that is the build process for the site, I would’t be surprised if there were a few.
Research Interests
Optimization problems in stochastic/statistical contexts; Calculus of variations; Optimal transport; Mathematical theory of machine learning; Computational methods
Undergrad materials
Classes and Thesis
A list of the all the math/physics/CS courses I took in undergrad can be found here.
My undergraduate thesis (Where the Wild Knots Are) can be found here, or alternatively here.
Salient Term Papers
I feel a strange mixture of pride and shame in admitting that almost all of each of the papers below were written in single nights. I’m not sure whether this is more an indictment of my lack of foresight or a testament to a pretty insane ability to speed-write under pressure, but either way it seems in keeping with the aesthetic of haphazardness that the name “bed math and beyond” connotes.
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Dynamical Systems and Computability Theory Final project for Dynamical Systems (senior spring), co-written with Matthew LeMay. Basically, we looked at how Turing Machines can be encoded as Dynamical Systems.
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Calculations Involving Perturbed Orthogonal Matrices Final project for Advanced Linear Algebra (junior fall), co-written with Evan Liang. Basically, we tried to prove some bounds on error propogation in diagonalization when you treat a non-orthogonal matrix as if it were orthogonal. Evan deserves credit for ~3/4 of the proofs; I provided the remainder and also wrote almost the entire writeup.
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Basic Quantum Computing and Quantum Error Correction. Term paper for intro quantum (sophomore spring). This is one of my most impressive speed-writing feats — everything from page 5 onwards was written between ~5pm 04/24/2018 and 9:16am 04/25/2018, and I have the
gitcommit history to prove it. Despite that, I think the exposition remains fairly lucid. The intended audience was other students in the course, so the paper should work as a gentle introduction to quantum error correction for people with a background in at least one of {linear / abstract algebra, basic quantum mechanics}. -
Artifical Grammar Learning & Formal Language Theory. Term paper for Intro Linguistics (junior fall). I was simultaneously enrolled in Computability and Logic at the time, so I tried to bring the content from the two classes together in the paper.
Some notes from classes
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Homology Theory Notes. A document of notes I took during my reading course in Homology Theory (junior spring). As with my category theory notes, these aren’t very polished. This is because I only did writeups when I had extra time after readings / exercises / stopping to smell the homological roses.
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Representation Theory Notes. Notes from the first 3/4 of my Representation Theory class (junior spring). Stopped working on this towards the end, as I started becoming embroiled in final projects. The parts that are there follow the exposition in Sagan for the most part, just being a little more explicit in proofs and such.
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Pset writing style guidelines for Topology. Junior spring, I was the grader for Harvey Mudd’s Topology class. Prof. Su wanted to make writing style a significant factor in the grading scheme, so I created this document to help students understand what we were looking for (and also help myself standardize my feedback).
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Notes from my reading course in Category Theory and Topology Junior fall. Same deal as the homology theory notes.
Misc math-flavored things
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A mosaic of all prime knots with crossing number up to 11. Generated with a knot-drawing algorithm co-developed with Jon Hayase.
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A talk I gave on the Euler-Lagrange Equation. If you have adobe reader, there are some really nice animations embedded in the beamer presentation that you can view.
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Some knot animations. Generated using 3Blue1Brown’s animation library, manim.
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A horrifically inefficient implementation of Conway’s game of Life on a non-uniform tiling of polygons. First, let me defend myself here: when I wrote this, I was fresh out of my very first CS class, and did not know that there were graphics libraries other than Python Turtle. Yes, that’s correct: the entire game board (which extends far, far beyond the portion shown in the video) is drawn using Python Turtle. This is part of why it takes multiple seconds to update each frame.
On an implementation level, there were some interesting abstractions. First, in order to store our data as a grid, we defined a unit cell object with which to tile our space. Then, we calculated adjacent unit cells, and finally adjacent polygons between the two unit cells. The thresholds for a cell living / dying were basically chosen randomly until we saw interesting patterns.
No idea if this version is turing complete as well or anything. Might be fun to look into.
Misc non-math
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A crude Schlieren system I made. Made by sneaking a converging mirror out of the Astronomy club’s big reflector telescope. Made it for my Photography class’s “photograph the invisible” project, in which I decided to go all in on literal interpretation since I’d spent the entire rest of the semester before seeing how far Prof. Fandell would let me stretch his prompts.
Since my final submission had to be a single still image, I wrote a script to extract frames from the video and arrange \(17^2 - 1\) of them into a grid. Also, since I wanted to maintain some level of overall cohesion to the piece, instead of placing them in the grid in order, I used an \(n=5\) hilbert curve to calculate where to place the photos, since conceivably this would do a good job preserving locality in 2D. I’ll try and upload the picture and my artist’s statement later, but first I need to find a place to host it (the image is huge).
In the meantime, maybe check out this tryptich I made with a dispersive prism Prof. Lynn dug out of a multi-decade-old interferometer for me!