Research

I've been working most recently studying Picard groups of perfectoid spaces, and more generally studying vector bundles and cohomology on perfectoid covers of varieties and schemes, specifically how to parametrize such objects and how they behave across characteristics (i.e., under tilting). Here is a selection of papers and preprints:

Research Talks

Here is a selection of past, present, and future invited research talks.

  • Joint Mathematics Meetings Mini Course: 3D Printing in Mathematics: January 3-4, 2022
  • University of California, San Diego, Number Theory Seminar: November 18 2021
  • University of Utah Representation Theory and Number Theory Seminar: October 6, 2021
  • Berkeley Undergraduate Number Theorey Conference: November 15, 2020
  • University of California, Berkeley, RTG Seminar in Arithmetic Geometry: April 20, 2020
  • Brown University Algebraic Geometry Seminar: November 22, 2019
  • Cornell University Algebraic Geometry Seminar: November 6, 2019
  • Dartmouth College Algebra and Number Theory Seminar: October 8, 2019
  • University of Washington Algebra and Algebraic Geometry Seminar: April 16, 2019
  • Boston University Number Theory Seminar: December 10, 2018
  • Columbia University Algebraic Geometry Seminar: December 7, 2018
  • Rice University Algebra and Number Theory Seminar: November 20, 2018
  • University of Arizona Algebraic Geometry Seminar: November 14, 2018
  • University of Oregon, WAGS Poster Presentation: October 6, 2018
  • MIT, Arithmetic Geometry, Number Theory, and Computation Mini Talk: August 2018
  • ICERM, Birational Geometry and Arithmetic, Poster Presentation: May 2018
  • University of California, San Diego, Graduate Research Presentation: May 2018
  • Arizona Winter School, Project Group Presentation: March 2017

Slides+

  • Slides from a talk on the developement of projectivoid geometry. Given at MIT's Arithmetic Geometry, Number Theory, and Computation workshop.
  • Poster given on the same subject at ICERM's Birational Geometry and Arithmetic workshop.