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 my undergraduate thesis, and hopefully this will soon include more papers.
• I've been writing software for mathematics research for years. My latest projects are OOKAMI and a much larger project written in C, Bestiary, which is a full scripting language with syntax inspired by LaTeX, containing hundreds of commands for math in many different domains. My ultimate goal for Bestiary is to implement all the math I have ever learned. Progress is moving very quickly, and Bestiary is already very usable as a toolkit for mathematical research and a full programming language.

What I'm doing

• Finishing a paper on the asymptotic sumset size of a certain family of sets, {i * p^j} for a prime p and i, j in [n].
• Diving deeper into combinatorics, quaternion algebras, finite group theory, and elliptic curves for research
• Studying real analysis, complex analysis, and measure theory for qualifying exams.

What I'll do

• This summer:
  • Prep course for the real analysis qual
  • Studying real analysis, complex analysis, and measure theory in depth
  • Finish my first combinatorics paper and work on related research projects
• Next semester:
  • Courses: elliptic curves, differential geometry, numerical analysis
  • Pass my last 2 qualifying exams
  • Start looking for an advisor

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
• 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)

What I'm doing

• Learning low-level programming, especially C, through a variety of methods
• Completing LeetCode problems regularly. I hit 100 recently!
• Working on toy languages and related C structures with Rainbow Dash (hi Dashie :3)
• Solving every exercise in the famous K&R book "The C Programming Language"
• Working tirelessly on Bestiary, and my other project ideas

What I'll do

• Implement all of the math I know into Bestiary
• Complete a full abstract algebra library in C
• 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
• 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
• Working on the new Nyartix fork of Nyarch Linux

What I'll do

• Figure out how to set up proper i2p mirrors for most of my services
• 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!
• 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
• Giving Japanese lessons sometimes
• 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 ノルウェーの森

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
• Reading Friedrich Nietzsche's The Antichrist
• Rereading The Fountainhead

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
• My top five anime series right now:
  1. 俺の妹がこんなに可愛いわけがない (Oreimo)
  2. Monster
  3. Death Parade
  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. Spice and Wolf
  3. Toradora
  4. 紫色のクオリア
  5. No Game No Life
• 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