Papers:
A Geometric Approach to Magic Squares of Squares, with Asher Auel (in preparation)
Presented a poster on progress at 2024 AGNES at Dartmouth poster session (AGNES Homepage - Dartmouth 2024, Dartmouth Hosts Major Algebraic Geometry Conference | Faculty of Arts and Sciences)
Gave a talk on further progress at the Young Mathematicians Conference 2025
Strata of Toric Hyperplane Arrangements, Zonotope Lattice Points, and the Bondal-Thomsen Collection, with Friedrich Bauermeister, Andrew Hanlon, Davis Painter, and Sair Shaikh (2507.14356), to appear in Involve. Result of 2024 SHUR at Dartmouth: SHUR | Dartmouth College
Gave a talk on results and necessary background information in the Dartmouth Algebra and Number Theory Seminar
Expository Notes:
I have been writing notes on classical p-adic Hodge theory for the past year, and will upload them here once they are finished!
I am writing notes on Galois cohomology for a DRP I oversaw, and combining them with a future DRP in p-adic analysis. The notes will be available here once those are completed!
I wrote course notes on category theory for the mini-course I taught, which is detailed on my teaching page. The notes PDF is available here. These notes cover:
Categories, functors, and natural transformations
Functor categories
The Yoneda Lemma, The Yoneda Embedding and representability
Universal morphisms and comma categories
(Co)Limits and their characterizations via products and equalizers
(Co)Completeness and continuity
Adjoint Functors and their interactions with limits
Abelian categories and some applications of category theory to computations of derived functors
And some exercises!
I wrote course notes on homological algebra for the unofficial course I taught, which is detailed on my teaching page. The notes PDF is available here. These notes cover:
Projective, injective, and flat resolutions
Derived functors
Ext and Tor (including the Baer sum, Kunneth formulae, etc)
Applications to commutative algebra (Hilbert's syzygy theorem, discussion of local rings via homological dimension, and the Quillen-Suslin theorem)
And many exercises!
I wrote a survey on GAGA and the Artin Comparison Theorem as a final project for a topics course on Hodge theory that I took in Spring 2025. A PDF is available here
Invited Talks:
Dartmouth Algebra and Number Theory Seminar (DANTS, Dartmouth College - Algebra and Number Theory Seminar), Tuesday, February 3, 2026
Talk Title: Introduction to p-adic Hodge Theory
Young Mathematicians Conference 2025 (Home | Young Mathematicians Conference)
Talk Title: Magic Squares of Squares
Slides are available here
Dartmouth Algebra and Number Theory Seminar (DANTS, Dartmouth College - Algebra and Number Theory Seminar), Tuesday, November 12, 2024, Hanover, New Hampshire
Talk Title: The Bondal-Thomsen Collection of a Toric Variety