Haoyang Guo

I am an assistant professor at the University of Minnesota.

I was an L.E. Dickson instructor at the University of Chicago from 2023 to 2025.

Before that, I was a postdoc at the Max-Planck-Institut für Mathematik in Beethoven's hometown, Germany, from 2021 to 2023.

I obtained my PhD in mathematics from the University of Michigan in 2021, where my advisor was Bhargav Bhatt.

I got my bachelor degree from the University of Science & Technology of China in 2016.

My research interests include algebraic geometry and number theory, especially p-adic geometry and p-adic Hodge theory.

Email: ghy "at" umn "dot" edu

Office: 352 Vincent Hall.

Address: 206 Church St. SE

Minneapolis, MN, 55455

Seminars/conferences that I co-organize(d)

@ University of Minnesota:

Arithmetic and Representation Theory (ART) Seminar, since 2025.

@ University of Chicago:

UChicago Algebraic Geometry Seminar, 2024 - 2025.
Workshop on Local Systems and Monodromy, Apr 6, 2025.

Papers/Preprints

Ogus's conjecture on F-isocrystals.

Preprint (2026), 91 pages, arXiv: 2606.22637.

The Tate conjecture for surfaces of geometric genus one -- embracing singularities, with Ziquan Yang.

Preprint (2025), 53 pages, arXiv: 2501.18541.

Pointwise criteria of p-adic local systems, with Ziquan Yang.

Preprint (2024), 86 pages, arXiv: 2409.19742; see also a Youtube video for a talk at Chicago.

Frobenius height of prismatic cohomology with coefficients, with Shizhang Li.

Preprint (2023), 42 pages, arXiv: 2309.06663.

Cohomological descent, de Rham comparison, and local acyclicity for some singular schemes, an appendix to

Rational p-adic Hodge theory for d-de Rham-proper stacks (by Dmitry Kubrak and Artem Prikhodko). Preprint (2022), 8 pages, arXiv: 2211.17227.

A prismatic approach to crystalline local systems, with Emanuel Reinecke.

Invent. Math. 236 (2024), no. 1, 17–164, 148 pages, published version: link, arXiv: 2203.09490.

Prismatic cohomology of rigid analytic spaces over de Rham period's ring.

J. Inst. Math. Jussieu (2025), 1-65, 65 pages, published version: link, arXiv: 2112.14746.

Crystalline cohomology of rigid analytic spaces.

Bull. Soc. Math. France, 153 (4), 2025, p. 831-948, 118 pages, published version: link, arXiv: 2112.14304.

Period sheaves via derived de Rham cohomology, with Shizhang Li.

Compos. Math. 157 (2021), no. 11, 2377–2406, 30 pages, published version: link, arXiv: 2008.06143.

Hodge-Tate decomposition for non-smooth spaces.

J. Eur. Math. Soc. (JEMS) 25 (2023), no. 4, 1553–1625., 73 pages, published version: link, arXiv: 1909.09917.

Teachings

@ University of Minnesota:

Math 8280, Topics in Number Theory: Weil Cohomology (instructor): Fall 2026.
Math 5248, Cryptology (instructor): Fall 2025, Fall 2026.
Math 5385, Computational Algebraic Geometry (instructor): Spring 2026.

@ University of Chicago:

Math 20250, Abstract Linear Algebra, two sections (instructor): Winter 2025.
Math 15910, Introduction to Proofs in Analysis, two sections (instructor): Winter 2024, Autumn 2024.
Math 24200, Algebraic Number Theory (instructor): Spring 2024.
Math 20310, Analysis in R^n I (instructor): Autumn 2023.

@ University of Michigan:

Math 105 (instructor): Fall 2017, Winter 2018.
Math 115 (instructor): Fall 2018, Winter 2019, Fall 2020 (remote), Winter 2021 (remote).
Math 216 (lab instructor): Fall 2019; course instructor: Sofia Piltz.
Math 498, Representation theory (grader): Winter 2017; instructor: Jessica Fintzen.
Math 602, Functional analysis (grader): Fall 2016; instructor: Sijue Wu.
Math 676, Algebraic number theory (grader): Fall 2016; instructor: Kartik Prasanna.

Expository Talks and Writings

On crystalline local systems, at University of Chicago, May 2025. Youtube video.
Boundedness of semistable sheaves, with Sanal Shivaprasad, Dylan Spence, and Yueqiao Wu.

Stacks Project Expository Collection (Lond. Math. Soc. Lect. Note Ser.), (2022), link, arXiv: 2112.03834.

On nearby cycle and perversity, an expository article on BBDG. Mar 2021. PDF.
HH, HKR; THH, and BMS 2, an expository article on (topological) Hochschild homology. May 2020. PDF.
Several approaches to Grothendieck duality. Jan 2020. PDF.
On the integral Hodge conjecture and integral Tate conjecture 3-folds. Dec 2019. PDF.
There is no abelian schemes over Z. Apr 2019. PDF.
Family of elliptic curves, and Serre-Tate theorem. Jun 2019. PDF.
Introduction to the de Jong's Alteration. Dec 2018. PDF.
Riemann-Zariski spaces and Nagata’s compactification. Oct 2018. PDF.
A note on de Jong’s conjecture. Jun 2018. PDF.
A mini-course on crystalline cohomology. Jun 2018. PDF.
F-finite modules. Mar 2018. PDF.
Note on finiteness properties of D-modules. Nov 2017. PDF.
"Spreading out” and its applications. Feb 2017. PDF.

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