Haoyang Guo
I am an L.E. Dickson instructor at the Univeristy of Chicago. Before that, I was a postdoc at the Max-Planck-Institut für Mathematik in Beethoven's hometown, Germany, from 2021 to 2023.
I am interested in algebraic geometry and number theory, especially p-adic geometry and p-adic Hodge theory.
I obtained my PhD in mathematics from the University of Michigan in the spring, 2021, where my advisor was Bhargav Bhatt. I got my bachelor degree from the University of Science & Technology of China in 2016.
Email: ghy "at" uchicago "dot" edu
Office: 332 Eckhart Hall.
Address: 5734 S. University Ave.,
Chicago, IL. 60637
Papers/Preprints
Frobenius height of prismatic cohomology with coefficients, with Shizhang Li.
Preprint (2023), 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), arXiv: 2211.17227.
A prismatic approach to crystalline local systems, with Emanuel Reinecke.
Inventiones Mathematicae, Volume 236, pages 17–164, (2024), published version: link, arXiv: 2203.09490.
Prismatic cohomology of rigid analytic spaces over de Rham period's ring.
Preprint (2021), arXiv: 2112.14746.
Crystalline cohomology of rigid analytic spaces.
Preprint (2020), arXiv: 2112.14304.
Period sheaves via derived de Rham cohomology, with Shizhang Li.
Compositio Mathematica, Volume 157, Issue 11, November 2021, pp. 2377 - 2406, published version: link, arXiv: 2008.06143.
Hodge-Tate decomposition for non-smooth spaces.
J. Eur. Math. Soc. 25 (2023), no. 4, pp. 1553–1625, published version: link, arXiv: 1909.09917.
Teachings
@ University of Chicago:
Math 24200, Algebraic Number Theory (instructor): Spring 2024.
Math 15910, Introduction to Proofs in Analysis, two sections (instructor): Winter 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 Writings
Boundedness of semistable sheaves, with Sanal Shivaprasad, Dylan Spence, and Yueqiao Wu.
Stacks Project Expository Collection (London Mathematical Society Lecture Note Series), (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, from a talk at Michigan. Dec 2019. PDF.
There is no abelian schemes over Z. Apr 2019. PDF.
Family of elliptic curves, and Serre-Tate theorem, from a talk at Michigan. Jun 2019. PDF.
Introduction to the de Jong's Alteration, from a talk at Michigan. Dec 2018. PDF.
Riemann-Zariski spaces and Nagata’s compactification, from a talk at Michigan. Oct 2018. PDF.
A note on de Jong’s conjecture, from a talk at Michigan. Jun 2018. PDF.
A mini-course on crystalline cohomology. Jun 2018. PDF.
F-finite modules, from a talk at Michigan. Mar 2018. PDF.
Note on finiteness properties of D-modules, from a talk at Michigan. Nov 2017. PDF.
"Spreading out” and its applications, from a talk at Michigan. Feb 2017. PDF.