Mathematical programming, algebra, representation theory, cryptography, combinatorics, numerical analysis, and more. Most of my academic interests revolve around mathematics, including most of my programming projects. I majored in mathematics as an undergraduate, and am currently a mathematics PhD student. I'm currently interested in many different subjects, but they often revolve around algebra and computation in some way.

What I've done

• Undergraduate courses taken:
  • Calculus I-III, Linear Algebra (2 courses)
  • Differential Equations (2 courses), Real Analysis (3 courses), Complex Analysis
  • Topology, Abstract Algebra, Algebraic Geometry
  • Number Theory, Probability and Statistics (2 courses), Dynamical Systems
  • Mathematical Logic, Cryptography
  • Supervised / honors projects in number theory and numerical PDEs
  • Many related courses in physics and computer science
• Graduate courses taken:
  • Abstract Algebra (graduate level)
  • Algebraic Number Theory (2 courses), Quaternion Algebras
  • Foundations of Mathematics, Reverse Mathematics
  • Commutative Algebra, Representation Theory (finite groups + Lie groups and Lie algebras)
• The mathematical research I've done so far can be found on the Research page. Currently this includes only my undergraduate thesis and my paper on quasilinear Cayley–Dickson multiplication, but it should continue to grow quickly over the next few months!
• I've been writing software for mathematics research for years. My projects this year are the additive combinatorics library OOKAMI, a full LaTeX-based scripting language and GUI application for advanced mathematics written in C, Bestiary, a general C library for arithmetic and algebra in Cayley–Dickson algebras, Quaternionic, and an implementation of a fast algorithm for multiplication in Cayley–Dickson algebras, fastCD.

What I'm doing

• Working on research in arithmetic complexity, algorithms, algebra, Cayley–Dickson and Clifford algebras, additive combinatorics, and more
• Taking courses in real analysis and measure theory, point-set and algebraic topology, and convex optimization this semester
• Learning new math every day

What I'll do

• Post two follow-up papers to my paper on quasilinear Cayley–Dickson multiplication, one which focuses on proving bounded-coefficients optimality and one which extends the algorithm to a larger class of algebras
• Finish and post two papers I'm working on in additive combinatorics, one of which I've been working on since February
• Keep following new research leads and refine my AI-heavy research workflow
• Learn from my classes and continue to improve my fundamentals

Algorithms, low-level languages, mathematical programming, C, language design. I'm very interested in low-level programming, especially C. Most of what I program is somehow related to mathematics.

What I've done

• Finished a minor in computer science as an undergraduate. Courses taken:
  • Data Structures and Algorithms (2 courses), Systems Programming, Numerical Algorithms
  • Quantum Computing (2 courses), Cryptography
• Taking graduate level computer science courses on data science, data structures and algorithms, and more
• Completed dozens of programming projects ranging in scale and scope, available on my git page
• Completed over 100 LeetCode problems, mostly in C and some in Python
• Wrote libraries for efficient computations with quaternion, octonion, and general Cayley-Dickson algebras (Quaternionic; fastCD)
• Added most of the foundational math I know to Bestiary and released it in May as v2.0.0

What I'm doing

• Learning low-level programming, especially C, through a variety of methods
• Taking a break from LeetCode, but I plan to return someday soon!
• Working on fastCD and planning eventual updates to Bestiary

What I'll do

• Implement all of the math I know into Bestiary
• Continue to develop software for efficient algebraic computations
• Become more experienced with numerical analysis and learn to implement more numerical algorithms

As a GNU/Linux enthusiast who loves to manage large integrated systems, I've enjoyed self-hosting for many years. My first real experience was hosting hidden services using Whonix when I was 17, but now I host a wide variety of services, and I look forward to maintaining them for years to come.

What I've done

• Used virtual private servers and software like NGINX to host static websites (like this one)
• Set up reverse proxies to protect my personal network
• Hosted Matrix servers and other federated social media platforms
• Designed a robust network of services running on a physical server I enjoy maintaining
• Managed relational databases with SQL, including PostgreSQL and SQLite
• Set up over a dozen services at my main website, keimai.space, with a Tor mirror for every web service
• Design and host the tanuki-cd.com and artificex.tech websites
• Contributed to NyarchKDE and created the "NyarchLibre" Nyarch GNUwU/Linux-Libre fork of Nyarch Linux

What I'm doing

• Maintaining my services at keimai.space
• Working on this website
• Continuing to find ways to manage my services more effectively, including how to trim the size of my Synapse server

What I'll do

• Figure out how to set up proper i2p mirrors for most of my services (eventually...)
• Find more services to host
• Help other ponies learn to self-host too

Japanese, German, Chinese, and what languages have in common and where they differ. I'm mostly interested in the Japanese language, which is my second and my favorite language. I'm currently learning German and Chinese, but at a slower pace than Japanese.

What I've done

• Learning Japanese since March 2022
• Passed the JLPT N1 in winter 2025--that was fun!
• Gave private lessons in Japanese for nearly half a year
• There's a long list of books I want to read and anime I want to watch, but I've already read and watched a lot more Japanese media in the native Japanese than I have in English.

What I'm doing

• Using Japanese to engage with otaku / weeb culture via watching anime, reading light novels and manga, listening to great music, and having experiences in Japanese that are hard to localize in other languages
• Learning German and Chinese, but at a slower pace than Japanese
• Enjoying occasional bouts of intensified interest in German and Chinese as I experienced early in my Japanese journey...and still do today!

What I'll do

• Learn German and Chinese thoroughly over the next few years
• Continue to learn more Japanese, and expand the amount of books and anime series I have completed in Japanese.

Philosophy has been an interest of mine from my young adult life on. Depending on the subject (and perhaps on the time in my life), philosophy has been both an intellectual interest pursued out of stimulation and pure enjoyment, and one serving a very essential need for me and being pursued as a necessity of life. As for literature, I find it to be a window into the human psyche, both into that of the author, and the minds of the characters.

What I've done

• Returning often to Ayn Rand, Aristotle, Friedrich Nietzsche, Max Stirner, Jean-Paul Sartre, Bertrand Russell, and many more
• Reading favorite novels and genres too numerous to list in their entirety here
• Finding The Fountainhead, Atlas Shrugged, Stranger in a Strange Land, Crime and Punishment, and The Plague especially meaningful
• Read some amazing Japanese literature, such as 博士の愛した数式 (yay math) and 人間失格

What I'm doing

• Engaging with philosophy both as an intellectual interest pursued out of stimulation and pure enjoyment, and as a necessity of life
• Continuing to engage with Ayn Rand and Friedrich Nietzsche directly and indirectly
• Strengthening my metaphysics, epistemology, and philosophy of mathematics and returning to metaethics

What I'll do

• Read through a selection of works from the Western canon
• Expand my literary horizons when I am able to read German classics and modern Chinese literature in their native languages
• I have a physical copy of 肩をすくめるアトラス (Atlas Shrugged in Japanese) and I intend to read it this year!!

I've been interested in anime and related media in some way for most of my life. Whether it's anime, manga, light novels, visual novels, or VTubers, I enjoy engaging with Japanese media of all kinds, and I love to be a part of the community surrounding it.

What I've done

• Watched dozens of anime series, some of them over half a dozen times; see my MAL profile to see what I've been watching
• My top five anime series right now:
  1. Steins;Gate
  2. Berserk
  3. Oreimo
  4. Spice and Wolf
  5. Made in Abyss
• Enjoyed a variety of light novel series in Japanese
• My top five favorite light novels:
  1. Oreimo
  2. No Game No Life
  3. Spice and Wolf
  4. Toradora
  5. 紫色のクオリア
• Watched VTubers play the Japanese localization of Undertale dozens of times for some reason :3

What I'm doing

• Actively reading through my favorite light novel series and watching multiple new anime series each month
• Collecting otaku merchandise and literature

What I'll do

• Possibly visit anime conventions in the future
• Maybe really get into VNs one day