Hello blog! This blog is the start of a new adventure. This may sound a bit overromantic, but I mean that I am looking forward to writing more. Earlier I enjoyed writing a lot, but as I got older and fell into more and more mathematics and responsibilty and got less time, writing up ideas and things I learned felt more like work than fun. I hope this blog may contribute to a change.
Before anyone starts asking sneaky questions; yes, the photo on the header is some bubbly stock-template-type photo I found.
Why make a blog?
I sometimes read blogs, tweets and other types of posts from different mathematicians, but to me it always seemed kind of far-fetched to make a website and actually do the writing myself. Why? There are always soul-crushing questions to be answered. Who would read it? I don’t know! What would I write about? I don’t know! If I could answer these, do I even know how to make a blog/webpage? Nope!
Over the last years, I have been reading a lot of mathematics, but the majority of the topics I briefed over have been forgotten. Some of the main ideas clung to me, but I couldn’t exactly lecture anyone without doing a substantial amount of recapping. Therefore, writing small posts about the topics I am exploring may certainly help, as I need to process the topics to a deeper level if I am going to explain them easily.
With this, I roughly know what I’m writing about, and I know that I am mainly doing it for my own sake. Of course, if anyone wants to read my posts, that is fun, and if I can inspire anyone to learn more mathematics, that is beyond fun!
To actually build up “the courage” to learn how to make a blog, was then the last part of my quest. Luckily, my friend Torgeir started his own mathematical blog a few years ago, which is a blog I often stop by to read. He helped me set up the basic GitHub-Hugo-driven format in less then two hours, and I am quite convinced I would have spent at least two weeks trying to navigate through the web of possibilities without his help, so I extend my deepest gratitude to him for that. His blog, which I recommend to everyone interested in mathematics, or more particularly algebraic topology, can be found in the links section.
Who am I then?
As you may have guessed, I am a mathematician. More precisely, I am a Norwegian student in mathematics at NTNU, and at the time of writing this blog post (Jan 2022), I am in the middle of my fourth year. That is, I started my bachelor’s degree in 2018, finished it in 2021 and started my master’s degree, which I expect to finish in 2023. My name is Elias Klakken Angelsen and I (mainly) do algebraic topology. When I am not messing around (e.g. working, reading, writing, acting) at NTNU, I enjoy a lot of different activities (e.g. bouldering and sailing). You can read more about me here.
What will I be writing about here?
Ok, so this is a blog about mathematics (mostly), but what does that mean? Well, to answer systematically, on the documents page, you can find stuff that I have been writing up before, slides and/or shitty notes from talks I have held, and even the articles I have written in the student association newspaper $\Delta t$.
The regular posts on the other hand, will vary, both in length, topics covered and how often they are posted. At the moment, I plan on exploring different aspects of mathematical physics, geometry, algebraic topology, homotopy theory, category theory, higher category theory (e.g. $\infty$-categories), topological data analysis and other funky topics I find interesting or need for my future thesis work. We may also encounter posts about statistics and data analysis as I am following a course on spatial statistics and have taken courses on topological data analysis and statistical learning in the past, as I find these topics quite interesting. There may also be examples of totally different topics, like acting, sailing, cooking, writing, etc.. I’ll admit, the mathematical posts are probably going to dominate, but we’ll see.
To give a few examples, the parts on mathematical physics will surely require an understanding of the aspects of differential geometry (e.g. manifolds, curvature, differential forms) and bundle theory (e.g. fibre bundles, principal $G$-bundles). This may (and should) also bring us into physics territory (e.g. quantum field theory, particle physics, relativity), where we may encounter other branches of mathematics/geometry (e.g. symplecitic geometry/topology as a mathematical theory of classical mechanics).
I am also writing a master thesis supervised by Gereon Quick in about a year, which I plan to dedicate a few posts to when working on it. The overarching theme will be Differential Cohomology, and posts about my thesis work will surely take us through the realm of differential geometry and the realms of $\infty$-category theory, stable homotopy theory and string theory, to mention a few. Maybe I’ll also include a post or two (or $n$ for $n \in \mathbb{N_0}$) about the work I did on my bachelor thesis. This would take us on a path through the basics of functional analysis, operator algebras and even time-frequency analysis, but it could also yield some interesting detours to noncommutative geometry and generalisations of topological techniques (e.g. operator $K$-theory).
Honestly, I have a lot of ideas (way too many). I can’t promise to write about any one of these, but I’ll try to cover a reasonable amount of topics. The posts will probably not be in any logical order either, as I know I plan a post on Joyal’s theorem from $\infty$-category theory in a few weeks due to the fact that I am holding a presentation on the topic for a master/phd seminar. In that post, I may bluntly assume that the few readers of this blog know a lot about category theory, and maybe also the fundamentals of $\infty$-category theory. Don’t despair! This level of preliminaries will not be the standard of the blog posts (I hope). As mentioned earlier, it would be beyond fun if I could inspire any subset of the (potentially empty) set of readers I have, and if I start off at a master-to-phd level in mathematics as preliminaries, this blog would not necessarily be inspiring (nor rewarding for myself).
Which posts get the honor of starting the mathematical bonanza (or bohnanza), remains to be seen. The next weeks I’ll spend some time constructing the different pages of this blog and planning the different projects I’m working on this semester. For now, let’s part ways with some links to the other interesting things you can look at, such as the documents page, Torgeir’s great blog and the Silence Project documenting Adam Ondra’s incredible climbing project, Silence, at Flatanger in Norway.