Notes
One of my favourite ways to spend time is to wrestle with an interesting mathematical problem. When the dust settles, I sometimes turn the scribbles into a more readable note. Here are some of those notes, along with a few term papers and reports. A 🔒 marks a note I no longer update.
Studying quantum field theory involves plenty of do-it-yourself calculations. In my QFT notes, I work through some of them in detail. This is a working draft, with some unfinished sections. [Last Update: Oct 2024]
🔒 My electrical engineering bachelor’s thesis, written in Persian, is titled “Phase Transitions in the Community Detection Problem: An Information Theoretic Approach”. [2021]
A term paper I wrote on rigid-body motion in relativistic physics. [Last Update: Jul 2021]
My general relativity calculation notes, still a working draft, include most of the work from my 2019 physics bachelor’s project. [Last Update: Dec 2022]
🔒 The Quasi-Inversion project led to several little lemmas; this note contains one of them. [Last Update: Feb 2021]
It is easy to make a paper cylinder but impossible to make a paper sphere. “What is the general rule here?” I asked Behzad, my high school friend, and he came up with a rather beautiful conjecture. This note proves a generalised version of it. It also raises a few questions I haven’t settled; see the Problems page. [Last Update: Apr 2019]
🔒 A playful toy model of wealth and generosity. It began as a joke and remains an unfinished modelling exercise. [Last Update: 2017]
🔒 I’ve long been interested in sphere packing. This is a revised version of a Persian review I published in 2017. [Last Update: 2017]
🔒 My Quantum Mechanics II term paper on the Lamb shift. [Last Update: 2017]
Suppose you have noisy data in 1,000 dimensions, but the underlying points lie on a curved manifold of much lower dimension—say seven. How would you estimate that intrinsic dimension? This working draft explores a method I developed in 2017. [Last Update: 2017]
🔒 My Fluid Dynamics term paper on Kolmogorov’s 4/5 law.
🔒 The “wag the tail” numerical method in Griffiths’ quantum mechanics textbook caught my attention, so I used it to calculate the energy levels of a particle in an infinite triangular well. [Last Update: 2015]