This page collects some writing I have done in the mathematical sphere.

Preprints

  1. Falkowski, D., Lidgren, C-F., Conjugating by singular operators: On the boundedness of similarity transforms near singular points.

    arXiv2410.19161

  2. Troedsson, E., Falkowski, D., Lidgren, C-F., Wendt, H., Carlsson, M., On joint eigen-decompositions of matrices.

    arXiv2409.10292

Notes

Sometimes I write notes on topics I’m interested in. They are not polished, and I rarely read them again after writing them. Therefore, expect that they should not be taken too seriously.

Lecture notes. Available here. An assortment of lecture notes, primarily on category theory, in preparation for mostly private lectures to some friends. Don’t have good name for it because it’s not a focused project. Active work in progress.

Final objects in \(\infty\)-categories. Available here. Follows Cisinski’s 2019 book. Written as lecture notes in preparation for a talk held in the introductory branch of a learning seminar on higher categories, organized by Bernhard Keller and Gustavo Jasso.

Commutative algebra. Available here. Notes based on Miles Reid’s book on commutative algebra. I wrote them while studying for a commutative algebra course (MMA330) taken at Göteborg University. I never quite finished them, as I didn’t end up needing to.

Tensor algebras & polynomial rings. Available here. A very brief note that I wrote to help a friend of mine understand tensor algebras. I think there may be slightly unconventional notation in it.

BSc. & MSc. Theses

  1. MSc. Thesis. My master’s thesis can be found here. For administrative reasons I don’t really understand, this is not on the LU Student Papers site yet.
  2. BSc. Thesis. My bachelor’s thesis can be found here or at:

    LUP9061112

Note. My bachelor’s thesis has many mistakes in it, and I’ve been working on personal notes which significantly improve upon it. Unfortunately, they are not complete enough for me to be comfortable releasing them. Due to other obligations, it is likely there will be quite some time until that changes.