Samuel Moss

I am a senior undergrad at Caltech studying mathematics. My main interests are higher category theory, topos theory, and algebraic K-theory.

Research

These are some projects I have completed that are interesting but not (yet) arXiv worthy. :)

Sheaf Theoretic Framework for Ruled Colorings
[PDF] — I develop a framework for ruled colorings of graphs. The paper is also aimed to provide introductory example for topos theory.
Profinite Negligible Cohomology and the Inverse Galois Problem (with Eduardo Nascimento)
[PDF] — We develop the theory of negligible cohomology for profinite groups and discuss its applications for the inverse Galois problem.

These are the final (unpublished) reports from the Caltech Summer Undergraduate Research Fellowship (SURF). These may contain some typos.

SURF 2025 (Groundwork for Hodge-Refined Whitehead Torsion)
[PDF] — Mentor: Professor Aravind Asok. We work through some basic Hodge number computations and develop some of the basic theory for ring objects in the category of mixed Hodge structures.
SURF 2024 (Misc. Results in Negligible Group Cohomology)
[PDF] — Mentor: Professor Matthew Gherman. We compute the negligible cohomology over fields of nonzero characteristic, compute some eventually negligible calsses in cyclic and integral group cohomology, and prove some negligibility properties of the Bockstein homomorphism.

Notes from various lectures and projects:

Basics of (Pre)Sheaves (Lecture Notes)
[PDF] — Notes for a lecture I gave on (pre)sheaves in algebraic geometry.
Central Simple Algebra Notes (Class Notes)
[PDF] — Some notes on central simple algebras from Caltech Ma 120c.
Hodge Decomposition Theorem Notes (Lecture Notes)
[PDF] — Notes for a lecture I gave on the Hodge decomposition theorem.
Logic in Topos Theory (Lecture Notes)
[PDF] — Notes for a lecture I gave on the internal language of a 1-topos.
Types of Categories (Reference Sheet)
[PDF] — Definitions for some "common" types of categories.

Slides from some presentations I've given.

Internal Yoneda Lemma
[PDF] — Slides for a presentation on the internal Yoneda lemma.