Papers and Talks.

I have written the following papers:

I am working on the following papers:

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

I have given the following talks:

  1. Algebraic geometry seminar (University of Utah): 7 November 2023.
    Cotangent complexes of derived jet and arc spaces.

  2. Graduate student colloquium (internal): 30 August 2023.
    Bézout's theorem --- to infinity and beyond. [Notes]

  3. CATS: Commutative Algebra in The South (University of Alabama): 15 April 2023.
    Deriving differentials and derivatives.

  4. CARES: Commutative Algebra Regional Expository Seminar (virtual): 24 October 2022.
    Spectral sequences aren't scary (no, really!). [Slides]

  5. Graduate student colloquium (internal): 19 October 2022.
    Video game character creation is a moduli problem. [Notes]

  6. Graduate student colloquium (internal): 6 September 2022.
    Algebraic geometry for new grad students.

  7. URiCA: Upcoming Researchers in Commutative Algebra (University of Nebraska-Lincoln): 7 May 2022.
    Derived algebraic geometry and jet schemes.

  8. ARTS: Algebra and Representation Theory Seminar (University of Oklahoma): 1 April 2022.
    Derived algebraic geometry and jet schemes.

  9. Algebra seminar (internal): 4 February 2022.
    Derived algebraic geometry and jet schemes.

  10. Graduate student colloquium (internal): 26 January 2022.
    UARK GSC What is...? #1: Tropical geometry. [Notes]

  11. 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]

  12. CARES: Commutative Algebra Regional Expository Seminar (virtual): 12 October 2021.
    The module of Kähler differentials. [Slides] [Recording]

  13. Jet spaces / arc spaces learning seminar (University of California San Diego, virtual): 19 May 2021.
    Jets, arcs, and cylinders. [Slides]

  14. CARES: Commutative Algebra Regional Expository Seminar (virtual): 15 April 2021.
    Macaulay2 Panel. Joint with Michael DeBellevue, Alexander Duncan, David Smith.

  15. CARES: Commutative Algebra Regional Expository Seminar (virtual): 11 March 2021.
    Jet and arc spaces from a commutative algebra point of view. [Slides] [Recording]

  16. The Curry Seminar: Algebra and topology seminar (internal): 13 October 2020.
    The Silmarillion: K-Theory. [Slides]

  17. 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]

  18. Spectral sequence seminar (internal): 31 July 2019.
    Differentially bigraded algebras and spectral sequence constructions. [Slides]

  19. Spectral sequence seminar (internal): 25 July 2019.
    Perfectly balanced: Using spectral sequences to balance Tor and Ext, and the Universal Coefficient Theorem. [Slides]