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:
- Searching for Rigidity in Algebraic Starscapes (2021, Joint with Shuchang Xu, to appear in the Journal of Mathematics and the Arts).
- Untilting Line Bundles on Perfectoid Spaces (2021, to appear in International Mathematics Research Notices).
- On Picard Groups of Perfectoid Covers of Toric Varieties (2020, Submitted, joint with Anwesh Ray and Peter Wear).
- Projective Geometry for Perfectoid Spaces (Münster J. of Math. 14 (2021), 445–484).
- Projective Geometry for Perfectoid Spaces (2018, PhD Thesis, longer version of the paper above, including more exposition and foundation. Beware: Errors that were corrected or removed in the published version may still appear).
- The Combinatorics of Interval Vector Polytopes. (2012, E. Journal of Combinatorics, Joint with Matthias Beck, Jessica De Silva, Joseph Pruitt, and Amanda Ruiz.)
Here is a selection of past, present, and future invited research talks.
- Santa Clara University Colloquium: January 27, 2022
- Joint Mathematics Meetings Mini Course: 3D Printing in Mathematics: January 3-4, 2022
- Saint Lawrence University Colloquium: December 16 2021
- 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