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 defineContinue reading “An informal outline of Noncommutative Geometry (Part III)”
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 relevantContinue reading “Baker’s Theorem and the Class Number Problem (Part 2)”
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 blogContinue reading “An introduction to Conformal Welding”
Geodesics on Regular Polyhedra
As a roleplaying game enthusiast I spend much of my free time interacting with – or boring my friends with talks on – platonic solids. My interest in the geometry of the platonic solids was piqued by a Numberphile video concerning geodesics on platonic solids. Admittedly, my knowledge of geometry is lacking, and so IContinue reading “Geodesics on Regular Polyhedra”
A whirlwind tour through Quantum Field Theory to Conformal Field Theory
This is designed as a very casual introduction, there are many aspects which are brushed over and ignored. This is because either it isn’t specifically relevant or I didn’t want to bog down the post with unnecessary minutia when the motivation is just to give one an idea of the subject. There are no referencesContinue reading “A whirlwind tour through Quantum Field Theory to Conformal Field Theory”
Baker’s Theorem and the Class Number Problem (Part 1)
Disclaimer: This post is the first 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. Over roughly 3 posts, I aim to introduce Baker’s Theorem, the Class Number Problem, and then discuss how Baker’s methods solved part of the problem. InContinue reading “Baker’s Theorem and the Class Number Problem (Part 1)”
An informal outline of Noncommutative Geometry (Part II)
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. In the first part of this series, I mentioned that Noncommutative Geometry (NCG) can be rather opaque because the notionContinue reading “An informal outline of Noncommutative Geometry (Part II)”
A Discussion on (Non-)Unique Factorisation
Disclaimer: This post is a quick discussion of some number theory related things; it is not meant to be rigorous. Throughout, I take to be a base field and to be an extension of ; towards the end of the post will represent the Hilbert Class Field of . Recently, I’ve spent a lot ofContinue reading “A Discussion on (Non-)Unique Factorisation”
An informal outline of Noncommutative Geometry (Part I)
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. General Relativity might be one of the most beautiful and powerful theories produced by mankind to this day. However, itContinue reading “An informal outline of Noncommutative Geometry (Part I)”
Greetings and welcome to Non Sequitur!
In this blog, you will find posts from three PhD students that come from very different fields: mathematical physics and number theory. Our main purpose is to share things that we find interesting, that includes but isn’t limited to problems, paper and book reviews, scribbles from the pub, or anything else that draws our attention.Continue reading “Greetings and welcome to Non Sequitur!”
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