1Personal info (Info personnelle)

Current position

Postdoc at

Email

zhouhang DOT mao AT gmail DOT com

Office

3.16

I am a postdoc at Korteweg-de Vries Institute for Mathematics under Lenny Taelman. Previously, I was 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 and publications ((Pré-)publications)

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

2. Perfectoid rings as Thom spectra, Selecta Mathematica, 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 $A\twoheadrightarrow A^{\text{'}\text{'}}$, 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

5Teaching (Enseignement)

• 2020-2021

  • TD LU2MA220: Elementary Number Theory and Algebra (Algèbre et Arithmétique)

  • TD LU2MA211: Lebesgue integral on ${ℝ}^n$ (Intégrale de Lebesgue sur ${ℝ}^n$)

• 2019-2020

  • TD LU2MA250: Series and integrals (Séries et intégrales) {non math major}

  • TD LU2MA122: Linear and bilinear algebra (Algèbres linéaire et bilinéaire IIa)