Eiko

PhD Candidate in Pure Mathematics
Research: Number Theory · p-adic Chabauty–Coleman methods

Overview

I am a PhD candidate in pure mathematics working in number theory, with a focus on p-adic Chabauty–Coleman methods. Alongside research, I build high-performance software (primarily in Haskell) and write educational material in abstract algebra and probability. I have written 100k+LOC of Haskell.

Research Interests

My current research direction centers on p-adic methods for studying rational points, especially Chabauty–Coleman style techniques.
I am particularly interested in extending Chabauty–Coleman methods using \(p\)-adic differential equations, aiming to broaden the scope of problems where t…

(The summary was written by GPT, for archiving the debug process)

Debugging a Bluetooth Speaker on Arch Linux: A2DP Broken, mSBC Works

Problem

I connected a Bluetooth speaker on Arch Linux and saw several profile choices in the desktop Bluetooth/audio UI:

• Audio Gateway
• Headset Head Unit (CVSD)
• Headset Head Unit (mSBC)

The observed behavior was:

(This document is generated by GPT for me to find interesting stuffs to learn at)

# Advanced Routes for Learning Functional Data Structures

This document is about **learning routes**, not just a catalogue of named structures.

The point is not merely to know that some data structure exists. The point is to learn a few strong design principles so that, when a new workload appears, you can design a representation that fits it.

A good way to think about a data structure is:

* **workload**: what operations matter, and with what frequency?
* **representation**: what shape of data can encode the state?
…

抹茶曲奇🍪

• 100 g of unsalted butter
• 50 g of icing sugar
• one yolk
• 180 g of self-rising flour or all purpose flour （过筛）
• 12 g of Matcha powder （过筛）
• Put it in the fridge for 1 hour

第一次尝试的时候黄油有点画了导致上模具的时候很容易被破坏掉图案。 另外可能是使用了自发面粉，上烤箱里之后饼干变得非常的大导致图案非常的不清晰。 第二次尝试保留原配方，但这一次在冰箱里冷冻的时间长一些，经测试可以上模具。 自发面粉做出来的口感更好，但是无法上复杂的模具。

Your first Haskell project: building a monadic parser combinator library

The goal of this project is to build our own parser library from scratch.

You will understand how monads work by building your own Parser monad! and its actually useful + beautiful!

The first step is to understand what a ‘Parser a’ means

a value of type ‘Parser a’ is a ‘runnable computation’ that can consume a String or a part of String, and produce a value of type ‘a’ along with the remaining unconsumed String.

newtype Parser a = Parser { runParser :: String -> Maybe (a, String) }

i.e. if it succeeds, it consumes part of the input String and produces a value of type ‘a’ along with the remaining unconsumed String. If it fails, it returns Nothing.

for example, we can d…

$$
% For comments
\definecolor{amethyst}{rgb}{0.6, 0.4, 0.8}
\definecolor{atomictangerine}{rgb}{1.0, 0.6, 0.4}
\definecolor{burgundy}{rgb}{0.5, 0.0, 0.13}
\definecolor{byzantine}{rgb}{0.74, 0.2, 0.64}
\definecolor{caribbeangreen}{rgb}{0.0, 0.8, 0.6}
\definecolor{carrotorange}{rgb}{0.93, 0.57, 0.13}
\definecolor{cinnabar}{rgb}{0.89, 0.26, 0.2}
\definecolor{darkcoral}{rgb}{0.8, 0.36, 0.27}
\definecolor{darkpastelpurple}{rgb}{0.59, 0.44, 0.84}
\definecolor{dodgerblue}{rgb}{0.12, 0.56, 1.0}
…

Postgres Boilerplate Script

This is the script I used for postgres boilerplate: setup a new database for your app in a second owo

Simple Non-Interactive Version

APP_USER="user"
APP_DB="user_db"
APP_DB_PASSWORD="password"

cat <<EOF

…

The following setup guide is produced by chatgpt, I will try it and verify it, modifying the parts that are not correct.

Windows: Haskell + h-raylib (raylib) Setup & Distribution Guide

This is a from-zero → working demo → shipping build checklist for getting raylib + Haskell (h-raylib) running on Windows, and packaging your game so users can run it by double-clicking.

Core idea: h-raylib typically vendors the raylib C sources via the package build, so you usually do not need a separate raylib installation. What you do need is a working Haskell toolchain + a working Windows C toolchain.

What you’re building (mental model)

Your shipped game will look like:

MyGame/

…

## Categorical Van Kampen Theorem

### Fundamental Groupoid

The **fundamental groupoid** $\Pi_1(X)$ of a space $X$ is a groupoid whose objects are the points of $X$ and whose morphisms are endpoint homotopy equivalence classes of paths $x\to y$.

* $\Ob(\Pi_1(X)) = X$

* $\Hom_{\Pi_1(X)}(x,y) = \{ x \to y \}/\sim$

There are some obvious properties:
…