Justin Alexander Bloom -- PhD Candidate, University of Washington

Contact

Email: justib8 AT uw DOT edu
Padelford Hall, C-552,
Department of Mathematics,
University of Washington.
Office hours Tuesdays, 4:30-6:00pm

Research

I am an algebraist. I am mostly interested in representation theory, and homotopy theory for its connections with modular representation theory of finite group schemes through tensor-triangular geometry.

CV

Here

Preprints and publications

Survey on Dieudonné theory (Expository, June 2025)
Families of Green rings for abelian restricted Lie algebras (Preprint, May 2025).
A tensor-triangular property for categories of representations of restricted Lie algebras (Preprint, December 2024).

Teaching

As of Autumn 2025, I am a TA for Math 504. Office hours Tuesdays 4:30-6:00pm.

Student Algebra and Representation Theory Seminar (StARTS)

Since Autumn 2025, I have organized Student Algebra and Representation Theory Seminar (StARTS), a graduate student seminar. See the main page here.

Mathematics for fun

I've been thinking about math for much longer than I've been a PhD student. Below are some old projects.

Fractional calculus

In 2019 I made a submission to Dr. Peyam, a mathematician-youtuber, explaining my idea for a Fractional analogue of the Taylor-series, replacing the sum with an integral.

As of 2024 the video continues to be discovered by young mathematicians. If you have found my website from Dr. Peyam's video, welcome! I will answer any questions you have by email. I have received deep questions that required a long response before, I recommend you read it here.

Cryptography

In 2016 I began my undergraduate studies at Oregon State University in computer science before I fell in love with pure mathematics.

Cryptography was the goal, and in 2019 I collaborated on a secure multi-party computation project using garbled circuits for Oregon State's REU program.