Hey! Welcome to the blog!
What is this blog for?
This website/blog was intially set up by the help of a friend of mine, Torgeir Aambø, who is doing a PhD in tensor-triangulated geometry and also runs a blog on mathematics. I recommend you to check it out. A link can be found on the links page.
The aim of the blog is to explore mathematics. For more information on what you can expect from the posts and the mathematical content, please see the initial post on the home page.
I’ll tell you a bit about myself.
My name is Elias. I studied mathematics at NTNU in Trondheim, and I finished my master’s degree in 2023. My main interests are within algebraic topology and homotopy theory, but honestly I am interested in a lot of topics ranging from mathematical physics to spatial statistics to the homotopy theory of operator algebras.
During my first years, I were mostly interested in operator algebras, and my passion for topology and algebra at the time drove me to write a bachelor thesis about the operator K-theory and Morita theory of certain structures from time-frequency analysis called noncommutative tori. This thesis was supervised by Franz Luef and can be found under the ‘documents ’ page here.
During my masters, I mostly focused on algebraic topology. I took courses and followed seminars on tensor-triangulated geometry, topological data analysis, infinity categories, differential forms, representation theory of finite groups, and even spatial statistics. Apart from coursework, I am mostly interested in chromatic homotopy theory, equivariant homotopy theory, as well as differential - and Hodge-filtered cohomology theories. The latter was the topic of my master thesis, which can be found under the ‘documents ’ page here.
My master thesis was supervised by Gereon Quick “On Differential Cohomology and Geometric Hodge-filtered K-theory”, and investigated exactly what the title says. It had two goals. The first was to showcase and give an overview of the field of differential cohomology, as there are many papers and great ideas out there, but relatively few textbooks or summarizing texts available. The second goal was to find a explicit geometric construction that satisified the axioms of a Hodge-filtered K-theory. This was done by utilising Multiplicative K-theory in the sense of Karoubi, and it provided an geometrically described example (which we postulate to be unique) of Hodge-filtered K-theory.
At the moment (2023/2024), I work as a Data Scientist in Oslo, and earlier I worked a lot at the university, both as a teaching assistant and as a student representative at the programme, institute and faculty level. If I am not doing anything “productive”, I am usually bouldering, acting (earlier with Gløshaugen Revy- og Teaterlag), quizzing, running, or sailing (/working on) the best sailboat in the Trondheim area (or now in the Oslo area), which is a 34 foot Sweden Yatch C34 called “SY MARLEN”.