1Personal info (Info personnelle)

Email: zhouhang DOT mao AT gmail DOT com

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.

Research 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).

2Preprints and publications ((Pré-)publications)

The PDF's here are supposed to be newer than the latest arXiv versions.

1. Noncommutative relative de Rham–Witt complex via the norm, arXiv:2410.05998, latest pdf

2. Equivariant aspects of de-completing cyclic homology, arXiv:2410.05994, latest pdf

3. Prismatic logarithm and prismatic Hochschild homology via the norm, arXiv:2409.04400, latest pdf

4. Revisiting derived crystalline cohomology, to appear in Bulletin de la Société Mathématique de France, arXiv:2107.02921, latest pdf

5. Perfectoid rings as Thom spectra. Sel. Math. New Ser. 29, 48 (2023). https://doi.org/10.1007/s00029-023-00851-0, latest preprint

3Notes

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 (deformation theory: 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

4Teaching (Enseignement)

• 2024 Spring, TA: Modules and categories

• 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)