Interests
My primary interests in mathematics lie in number theory and in particular arithmetic geometry, which studies arithmetic by applying insights from geometry and topology. More specifically, some topics that I especially want to understand are
- Cohomology theories in arithmetic geometry
- Rational points on varieties and algebraic stacks
- Enumerative geometry over arbitrary ground fields
- Galois representations, étale sheaves, and ramification theory
Outside my primary interests, I would also love to learn more about mathematical logic and representation theory. At heart, I am an algebraist, and I have general interests in all kinds of mathematics of an algebraic or “conceptual” flavor. I'm also interested in artificial intelligence, machine learning, and their interactions with mathematics.
Publications
Coming soon.
Notes
I write and continue to update self-contained notes on various mathematical topics. Here are some that I have written.
- Linear Algebraic Groups and Representation Theory (coming soon)
- Algebraic Curves and Abelian Varieties (coming soon)
- Algebraic Number Theory (coming soon)
Here are some on very specific topics which are on the shorter side.
- Brauer Groups (coming soon)