Math blog... maybe?

This is a blog on ANY subjects I’m interested in, including math, machine learning, musics, cubes, etc.

2024

Fermat’s cubic and Ramanujan’s tau function modulo 3

The goal of this post is to prove the following congruence: for primes $p \ne 3$,

Building Bridges: 6th EU/US Summer School & Workshop on Automorphic Forms and Related Topics

There was Building Bridges: 6th EU/US Summer School & Workshop on Automorphic Forms and Related Topics which is an annual 2-weeks conference for the topi...

Kazhdan-Lusztig Polynomials

The goal of this post is to introduce Kazhdan-Lusztig polynomials and its connection to perverse sheaves. It can be one of the pioneering example of geometri...

Weyl’s complete reducibility theorem for semisimple Lie algebra: homological algebra proof

In this article, we reproduce the proof of Weyl’s complete reducibility theorem:

Gan-Gross-Prasad conjecture: References

Here I give a comprehensive list of existing works on Gan-Gross-Prasad conjectures, for

Algebraic proof of modular form inequalities for optimal sphere packings

I uploaded a new paper on arXiv about modular form inequalities appear in the proof of optimality of $E_{8}$ and Leech lattice sphere packings by Viazovska a...

Relative Langlands Duality summer school & workshop at UMN

There was Relative Langlands Duality summer school & workshop at University of Minnesota, which introduces the recent work by Ben-Zvi, Sakellaridis, and ...

Tate’s Thesis and Riemann-Roch Theorem

In this article, I explain the meaning of the following statement:

Solving olympiad geometry without human demonstrations

There are recent initiatives, including IMO Grand Challenge and AIMO that seek AI solving international mathematical olympiad problems and win a gold medal. ...

2023

Music I listened in 2023

End of 2023 is here. I want to share my favourite tracks and DJ sets that I’ve listened this year. Some of the tracks are released before 2023 - these are th...

A progress on Conway-Soifer conjecture

I recently wrote a paper on the Conway-Soifer conjecture with my friend Jineon Baek. The paper by Conway and Soifer is famous for holding the best record for...

New(?) proof of Bassel problem

In this post, we give a new short proof of the Bassel problem $\zeta(2) = \pi^2 / 6$ using Eisenstein series.

How to teach

Disclaimer: All the statements here are my own opinion. It does not reflect any organizations.

ICML 2023 Review

I just returned from Honolulu, Hawaii, where this year’s ICML was held. Although I do not major in ML, I attended to present my work on homomorphic encryptio...

Exceptional isomorphisms for low-rank general spin groups

In this post, we define general spin groups via Clifford algebra and give exceptional isomorphisms with other groups for low rank cases. Main references are ...

LoRA: Low-Rank Adaptation of Large Language Models

In this post, we introduce the paper “LoRA: Low-Rank Adaptation of Large Language Models” by Edward Hu, Yelong Shen, Phillip Wallis, Zeyu Zhu, Yuanzhi Li, Sh...

Interesting applications of p-adic numbers

In this post, we will see some interesting applications of $p$-adic numbers. We will assume that readers are familiar with $p$-adic numbers and their basic p...

Image of a congruence subgroup is not always congruence

Let $G$ be a reductive algebraic group over $\mathbb{Q}$. Choose an embedding $G \hookrightarrow \mathrm{GL}_n$, and define

ChatGPT and Watermarking

In November 30, 2022, OpenAI released ChatGPT, and (at least in my opinion) it changed the world a lot, because of its standout performance. It can do a lot ...

Simple code snippet for an offline translation

I’m reading a French paper by Jacquet on the proof of Waldspurger’s formula using Relative Trace Formula. Since I’m completely new to the French, I’m reading...