Personal webpage (Page personnelle)$\ast$

 by Zhouhang Mao

 December 9, 2021

$\ast$. This document has been written using GNU TeXmacs; see www.texmacs.org.

## 1Personal info (Info personnelle)

Current position

Postdoc at Institut de Mathématique d'Orsay (Post-doctorant à l'Institut de Mathématique d'Orsay)

Email

zhouhang DOT mao AT universite-paris-saclay DOT fr

Office (Bureau)

Math 2O1

I am a postdoc at Institut de Mathématique d'Orsay, under Kęstutis Česnavičius' ERC Grant (and help, of course). Before that, I was a PhD student at Sorbonne Université, advised by Matthew Morrow. Before that, I was an international student at ENS. Before that, I was an undergrad at Fudan University.

Detailed CV.

## 2Research interests (Thème de recherche)

The interaction between topology and algebraic geometry: derived algebraic geometry (géométrie algébrique dérivée), algebraic topology (topologie algébrique), arithmetic geometry (géométrie arithmétique), algebraic $K$-theory ($K$-théorie algébrique), topological cyclic homology (homologie cyclique topologique).

## 3Preprints (Prépublications)

1. Revisiting derived crystalline cohomology, arXiv:2107.02921, latest pdf

2. Perfectoid rings as Thom spectra, arXiv:2003.08697, latest pdf

## 4Notes

1. Revisiting derived crystalline cohomology, Séminaire d'Arithmétique et de Géométrie Algébrique, Université Paris-Saclay, notes

2. Perfectoid rings as Thom spectra, Seminar of the algebraic topology group, Université Paris Nord, slides

Warning. There is a major mistake in these slides: the formulation of the deformation theory is incorrect. It should be formulated as the following: given an infinitesimal thickening $A↠{A}^{\text{'}\text{'}}$, the derived base change induces an equivalence from the category of formally étale $A$-algebras to the category of formally étale ${A}^{\text{'}\text{'}}$-algebras.

3. M2 Mémoire: Comparisons of different constructions in algebraic $K$-theory, pdf