I have written the following papers:

I am working on the following papers:

*Derived jets and arcs*. With Roi Docampo and Lance Edward Miller.*Non-representability of arithmetic arc spaces*. With Taylor Dupuy and Lance Edward Miller.*Isocrystals associated to arithmetic differential equations in algebraically closed fields*. With Lance Edward Miller and Arnab Saha.*Noncommutative resolutions of singularities in positive characteristic*. With Peter M. McDonald.

I have given the following talks:

- Algebraic geometry seminar (University of Utah): 7 November 2023.
*Cotangent complexes of derived jet and arc spaces*. - Graduate student colloquium (internal): 30 August 2023.
*Bézout's theorem --- to infinity and beyond*. [Notes] - CATS: Commutative Algebra in The South (University of Alabama): 15 April 2023.
*Deriving differentials and derivatives*. - CARES: Commutative Algebra Regional Expository Seminar (virtual): 24 October 2022.
*Spectral sequences aren't scary (no, really!)*. [Slides] - Graduate student colloquium (internal): 19 October 2022.
*Video game character creation is a moduli problem*. [Notes] - Graduate student colloquium (internal): 6 September 2022.
*Algebraic geometry for new grad students*. - URiCA: Upcoming Researchers in Commutative Algebra (University of Nebraska-Lincoln): 7 May 2022.
*Derived algebraic geometry and jet schemes*. - ARTS: Algebra and Representation Theory Seminar (University of Oklahoma): 1 April 2022.
*Derived algebraic geometry and jet schemes*. - Algebra seminar (internal): 4 February 2022.
*Derived algebraic geometry and jet schemes*. - Graduate student colloquium (internal): 26 January 2022.
*UARK GSC What is...? #1: Tropical geometry*. [Notes] - Graduate student colloquium (internal): 17 November 2021.
*What's on the mind of air traffic controllers and algebraic geometers? #2 (Blowing up points on the plane)*. [Notes] - CARES: Commutative Algebra Regional Expository Seminar (virtual): 12 October 2021.
- Jet spaces / arc spaces learning seminar (University of California San Diego, virtual): 19 May 2021.
*Jets, arcs, and cylinders*. [Slides] - CARES: Commutative Algebra Regional Expository Seminar (virtual): 15 April 2021.
*Macaulay2 Panel*. Joint with Michael DeBellevue, Alexander Duncan, David Smith. - CARES: Commutative Algebra Regional Expository Seminar (virtual): 11 March 2021.
- The Curry Seminar: Algebra and topology seminar (internal): 13 October 2020.
*The Silmarillion: K-Theory*. [Slides] - Graduate student colloquium (internal): 11 March 2020.
*What's on the mind of air traffic controllers and algebraic geometers? (An introduction to jet spaces)*. [Notes] - Spectral sequence seminar (internal): 31 July 2019.
*Differentially bigraded algebras and spectral sequence constructions*. [Slides] - Spectral sequence seminar (internal): 25 July 2019.
*Perfectly balanced: Using spectral sequences to balance Tor and Ext, and the Universal Coefficient Theorem*. [Slides]