## Hadamard states: Part I

Disclaimer: This post is part of a series about Hadamard. I do not pretend to be rigorous nor thorough. The main idea is just to cover (in a rather informal way) the main concepts. Within the framework of algebraic QFT (AQFT), the fields are the fundamental observables of the theory and are algebra-valued distributions. The…

## Baker’s Theorem and the Class Number Problem (Part 3)

Disclaimer: This post is the third of a set of three(ish) about Baker’s Theorem and the Class Number Problem. It is intended to be informative and not too rigorous. Find part one here and part two here! So, we’ve introduced both the Class Number One Problem and Baker’s Theorem, and now we’re going to try…

## The mathematics of weather prediction and why complaining about it won’t help

Welcome back to the blog, I am taking a break from talking about conformal field theories to rant (non-seriously, I’m too apathetic to actually care) about weather prediction. Specifically I would like to discuss the challenges we face when trying to accurately calculate long term weather forecasts. For far too long I’ve heard complaints about…

## Quantum Energy Inequalities, Part I

I am pretty sure that some of our readers must know of Sabine Hossenfelder, she is a really good researcher and communicator of science, make sure to check out her Youtube channel. A couple a weeks ago, she released a really good video with some exciting news: new developments in a certain class of warp…

## Analytic and numeric implementation of conformal welding

Previously we discussed conformal welding in a fairly general setting. I stated that it had a use in calculating probability distributions of smeared energy densities, my aim is for this post to set the last of the mathematical foundation before I can then delve into the consequences of this. As with last time I will…

## On Dirichlet’s Unit Theorem and the Class Group

So today, I’m going to write about something I’ve learnt that I think is really cool. Unsurprisingly, it’s related to the Class Group; I will get back to my set of posts on Baker’s Theorem and the Class Number Problem, think of this as a nice excursion. I might go quite fast over the basics…

## Geodesics on Regular Polyhedra II

In my previous post we explored the problem with drawing simple geodesics, beginning and ending at the same vertex, on the tetrahedron and octahedron. Today we tackle the beasts that are the cube and icosahedron. Relevant papers for this section are Fuchs & Fuchs 2007 [1] and Fuchs 2016 [2]. This post will be a…

## An informal outline of Noncommutative Geometry (Part III)

Disclaimer: This post is part of a series about Noncommutative Geometry. I do not pretend to be rigorous nor thorough. The main idea is just to cover (in a rather informal way) the main concepts. The fuzzy sphere is a really nice example of how the Noncommutative Gel’fand-Naimark Theorem (NCGNT) can be used to define…

## Baker’s Theorem and the Class Number Problem (Part 2)

Disclaimer: This post is the second of a set of three(ish) about Baker’s Theorem and the Class Number Problem. It is intended to be informative and not too rigorous. Find part one here! In this post, I’ll introduce the Class Number Problem, before (eventually) pulling these posts together and seeing how Baker’s Theorem is relevant…

## An introduction to Conformal Welding

Here we discuss the subject of Conformal Welding, the best resource on this is given by Sharon and Mumford in a paper titled “2D-Shape Analysis Using Conformal Mapping”, I will cover some of the material that is in that paper but it will be refined for my specific interest. As mentioned in my previous blog…

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