Department of Mathematics, Statistics and Computer Science
University of Illinois Chicago
Office: SEO 411
I am a Research Assistant Professor in the Mathematics Department at University of Illinois Chicago. I recently completed my Ph.D. from the University of Michigan, where I was advised by Karen Smith.
I work at the interface of algebraic geometry and commutative algebra. I enjoy thinking about non-Noetherian objects that arise in geometry and arithmetic (such as valuation rings and perfectoid spaces).
Winter 2019: Math 210 (the course website). Here is the website for my sections.
Here is a copy of my dissertation. Corrections are welcome!
Notes are subject to change without notice.
- Very rough notes (prepared for a Grad seminar at UMich) on a proof of a theorem of Kunz, characterizing regularity of Noetherian rings in terms of flatness of Frobenius, using the surprising homological properties of perfect rings. Based loosely on a talk given by Bhatt at Gennady Lyubeznik's 60th birthday conference, the notes are a more verbose version of the original proof appearing in a paper by Bhatt-Scholze.
- Notes on Huber rings for a learning seminar at the University of Michigan (Winter 2017). Last updated Feb 18, 2017. A new section was added on uniform Huber rings (not discussed in the lectures), following Bhargav’s discussion of uniform K-Banach algebras in his course. In particular, we prove equivalence of categories results generalizing [Bha17, Thm 9.7 and Cor 9.9].
- On a vanishing result in sheaf cohomology. An example is given of a non-quasicompact scheme that violates a vanishing result in sheaf cohomology that holds for certain quasicompact spaces [Stacks Project, Tag02UX]. This example can be interpreted purely topologically (without mentioning schemes), and is incorporated in the latter form in Tag0BX0.
- Notes from a summer mini-course I taught at Michigan on notions of singularities in prime characteristic in 2016. The notes have not been proof-read and do not cover a lot of material.