Longke Tang 唐珑珂

Email: longket [at] alumni [dot] princeton [dot] edu

I am a research member of the SLMath Program on Motivic Homotopy Theory in Fall 2026. After that, I will be a postdoc at MPIM.

I obtained my PhD in 2026 at Princeton University under the supervision of Bhargav Bhatt. I obtained my B.Sc. in 2020 at Peking University under the supervision of Ruochuan Liu.

Papers and preprints:

  1. Thesis. The P^1-motivic Gysin map. arXiv:2604.24888
  2. Slicing criterion for ind-smooth ring maps. arXiv:2404.17988
  3. Syntomic cycle classes and prismatic Poincaré duality, Compositio Mathematica 160.10 (2024), pp. 2322–2365.

Notes:

In English:

  1. fppf cohomology of smooth groups, explaining Grothendieck's theorem that the fppf cohomology and the étale cohomology coincide for smooth groups.
  2. Tensor products over nonunital rings depend on base categories. I found afterwards that it appears here independently as Example 2.10.7.
  3. Direct summand theorem by arc cohomology.

中文:

我的中文数学笔记基本都在香蕉空间上, 详见我的用户页. 我也在那儿写了不少百科条目.

  1. 凝聚态数学讲义.
  2. 对角线的妙用.

Talks:

  1. The P^1-motivic Gysin map (in Chinese), in Chongli, Hebei, China, on 2024-07-03
  2. The P^1-motivic cycle map, at HIM Trimester Seminar Series, on 2023-05-25.
  3. Prismatic Poincaré duality, at University of Copenhagen Algebra/Topology Seminar, on 2023-02-03.
  4. Prismatic Poincaré duality, at UCSD Number Theory Seminar, on 2023-01-19.

Others:

I have been learning to play carillon with Lisa Lonie, the carilloneur of the Princeton University Carillon, since summer 2021. Here is my recording from the summer 2022 Princeton Carillon Studio Concert, in which the three pieces are: More Black than White, composition by G. D'hollander; 《草原情歌》 (Love Song of the Prairie), Chinese folksong, arranged by M. Polak; and Sofðu unga ástin mín (Sleep, my young love), Icelandic Folksong, arranged by R. de Waardt.

I have also spent some time performing Xiangsheng (Chinese crosstalk) with some friends in PKU Students’ Quyi Association while I was in Peking University. Here is a version of the piece 《高人一头的人》 (One-Upper) that Yinbo Wang and I performed in 2019.