update, Jun 5, 2026

On this day, I seem to be a little bit caught up in my emotions and can't focus on working. It was a public holiday yesterday, Corpus Christi, and thanks to someone else who is not in the math department where I work, I was informed that I don't need to come to work. I came in anyways, and spent the afternoon wrestling with Macaulay2, before going home in the rain. But today, I can't get myself into the code. Instead, I gaze out at the still slightly rainy outdoors and follow my thoughts meandering through memories from this past year and the many years before that alike.

But enough of that high-register sort of speak. I'd like to give an update on what has been going on for the past couple months.

First, I neglected to write an IAP post. Or an end of fall semester post. But I think the culprit behind my lack of writing is that I neglected to write that IAP post. Paradoxically, I had both plenty of time and plenty of work at the time. I definitely could have made time to write, but I didn't. In short, that winter was spent serving as the academic chair to a dying (in the age of generative AI) Web Lab. What I, someone who has long since dived into the deep end of pure mathematics, am doing in such a computer-sciencey place as Web Lab is unknown to me. But I was doing that for the winter. I lectured in front of a lecture hall. I answered questions in office hours. It was a lot of fun. I like teaching.

As for the spring semester, you can go read Vestigial (https://listed.to/@angelofd3sth/71000/vestigial) for the first couple weeks. Foreseeing that I wouldn't get an A in the class (as I did in its precursor), I dropped Algebraic Geometry II and instead decided to review the contents of the first course. The aftermath is that I made my way through chapters 1 and 2 of Vakil with every exercise completed. I'm happily fluent in category theory. But am I happy with my mathematical progress this past semester?

"You know, shortly after you dropped, everything went slower and it was super manageable."

It must be a sign that it was a well-written essay, that I think back to the words that I typed in Vestigial. In times where my regrets begin to crowd by mind, I take a deep breathe in and remind myself that there is no need to be optimal all the time. It's arbitrary anyways, the line in which I draw between work and rest. Why not move it so that rest gets a little bit more time? At least I don't go to bed every night, worried that I didn't work enough and that if I don't sleep right now, I won't be able to work enough tomorrow, so worried that I wouldn't fall asleep. The traces of those sleepless nights are still with me, but I am able to tell myself "if I don't sleep tonight and tomorrow is terrible, then let it. I always have another day after that."

So that's where I was mathematically. I mean, it doesn't change the fact that I sorely wish I knew sheaf cohomology. Or homology and derived functors. But there are many things I wish I knew: homotopy theory, Lie theory, and so on and so forth. That would be pretty helpful for my research.

What am I doing now, you may be wondering? I'm currently in Germany as part of MISTI-Germany. I'm at the University of Duisburg-Essen and I'm working on a research project on local models of Shimura varieties, and when they are Gorenstein. I've only been here for two weeks and the project is going. The professor to graduate student ratio is high (I actually never know with these things, I suppose I mean to say that there are comparatively fewer grad students to professors than the US) and the people here never have to deal with undergrads asking for research projects, and so all of them are pretty happy to answer whatever questions I have. It's very nice; I eat lunch with them at the Mensa and listen to math gossip.

I've come to realize that math is all-consuming. There is just so much you have to learn, that you end up spending so much of your time working to be a better mathematician. You end up having to actively set aside time to work on hobbies. That's why I haven't been writing so much. That's why I'm putting down my clarinet.

I would like to write an elegy to my music career sometime. I hope it makes it out of my drafts. I won't say too much about that decision here, only that I like it enough to do it. I'm not in high school anymore; there's no such thing as a productive and unproductive hobby; if climbing the ranks of Valorant is what I like doing, then I should just let myself do it and have fun. Better than forcing myself to practice when all I do between playing pieces is doomscroll to forget the fact that I'm practicing. It's not like I'm playing to get into college.

As for writing, I think the biggest reason why I haven't been writing that much is that after taking the essay-writing class, I've just had higher standards for my writing. I want to write well-put-together personal essays and post that, instead of my regularly-scheduled word-vomit blogs (even though my essays turn out to be slightly edited word-vomits, but hey, I do think a lot about the structure when I do that word vomit). But writing is a practice, and you have to practice to get better at writing. And so I have to write these blogs. Besides, I really do have fun and enjoy writing. The more my brain realizes that I do have fun whenever I write, the more I want to write and tackle those bigger pieces.

Hopefully I am able to publish these bigger works in these coming months. In the meantime, you'll get the jumbled thoughts that didn't make it to a final draft.

Bis bald und Tschüssie~