#### Dehn invariant zero tetrahedra

A comprehensive list of currently-known tetrahedral families with Dehn invariant zero. This is the result of a UROP conducted with Prof. Bjorn Poonen and Kimi Sun.

Math & AI @ MIT

I'm an MEng student at MIT's Laboratory for Information and Decision System. I graduated in 2024 with a degree in Math (18) and AI (6-4) from MIT as well. Broadly speaking, I'm passionate about the interesection of theory and computation - using computation as a tool to discover and understand number theoretic patterns (computational number theory).

I am involved with Algeria's national mathematics olympiads, and I also previously served as problem staff at HMMT.

Here's my CV if you would like to have a look at it. A list of classes can be found here, while a list of projects can be found below.

The following are some resources I've written up over time.

A comprehensive list of currently-known tetrahedral families with Dehn invariant zero. This is the result of a UROP conducted with Prof. Bjorn Poonen and Kimi Sun.

In this group project, we analyzed the memory usage (in bits) needed to maintain an adversarially-resistant bloom filter, where resilience is defined in terms of a security game. We improved known lower bounds to get near-optimal memory usage in sublinear cases.

Notes on the discrete logarithm problem, particularly motivated by the Diffie-Hellman exchange protocol in cryptography. This was written as a final paper for 18.704 - Seminar in Algebra.

Notes on arithmetic functions and Dirichlet convolutions, particularly aimed towards motivating the latter as well as demysifying the Möbius inversion. I wrote this as undergraduate assistant for the Spring 2022 offering of 18.781 (MIT's elementary number theory class), taught by Prof. Ju-Lee Kim. I wrote these because I found that most textbooks' treatments of the subject to be relatively unmotivated and/or confusing. I had struggled for years with fully grasping what Möbius inversion was really about, and so I hoped that this would help students avoid the issue.

Notes from 18.112 on the modern proof of the prime number theorem, along with some elementary consequences of the theorem.

Elementary point-set topology notes in Andrew Lin's LaTeX package.

This is frankly just a prone-to-error summary of important formulae and definitions that I spiced up by including as much analysis as I could.

The following are some practical projects I've done over time, loosely organized by topic, along with a short description. Research projects are listed on my CV.

- JPEG Encoder

Implemented an efficient JPEG encoder which inputs an image in raw form as brightness values and outputs a JPEG image. - Separating Harmonies

Used frequency-domain methods to design a Python program which separates bass, melody, and harmony components of a 3-part harmony. - Echo Cancellation

Employed convolutional methods in the time domain to de-echo a real-life audio message. The same method was applied but in the frequency-domain for a more efficient implementation. - Note Detection in Chords

Converted a signal to the frequency-domain representation using Fourier transform, which was then analyzed to identify the corresponding notes in the original signal.

- Solver for CNF Formulae Implemented an efficient solver for Boolean satisfiability problems.
- Symbolic Algebra

Used Object-Oriented Programming (Python) to build a symbolic algebra system. *N*-dimensional Minesweeper
Wrote and improved Python code which simulates a playable

- CRIME attack against gzip compression

Conducted CRIME attack which infers the contents of a message by observing the change in size of the compressed payload. This attack specifically targeted the gzip compression algorithm. - Broadcast attack against RSA

Implemented the broadcast attack against the RSA: this exploits encrypting the same message under different public keys. - One-time pad encryption with same key

Theory teaches us that it is insecure to use the same key twice for symmetric encryption. This cryptanalytic attack demonstrates this: we use a library of known English words to completely retrieve two original message that were encrypted using the same key under symmetric encryption. - Memory Usage of Adversarially-Resistant Bloom Filters

In this group project, we analyzed the memory usage (in bits) needed to maintain an adversarially-resistant bloom filter, where resilience is defined in terms of a security game. We improved known lower bounds to get near-optimal memory usage in sublinear cases.

- Imaginary Quadratic Orders

Implemented an efficient algorithm to enumerate all imaginary quadratic orders of class number less than a given bound, assuming the Generalized Riemann Hypothesis. - ML Classification of Elliptic Curves

Trained machine learning models to predict the Sato-Tate group of elliptic curves using Scikit Learn.