Longke Tang 唐珑珂

Email: longket [at] princeton [dot] edu

I am a PhD student at Princeton University from 2021. My advisor is Bhargav Bhatt. I obtained my B.Sc. in 2020 at Peking University, where my advisor was Ruochuan Liu.

Papers and preprints:

  1. The P^1-motivic Gysin map. In preparation. Here is the slides on it that I made for Ruochuan Liu's workshop in July 2024 in Chongli, Hebei, China; it is therefore written in Chinese. See also my 2023-05-25 talk.
  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. Gysin maps for oriented P^1-spectra. This is outdated, as I now have a construction that does not need an orientation; see my 2023-05-25 talk.
  4. 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 cycle map, at HIM Trimester Seminar Series, on 2023-05-25.
  2. Prismatic Poincaré duality, at University of Copenhagen Algebra/Topology Seminar, on 2023-02-03.
  3. Prismatic Poincaré duality, at UCSD Number Theory Seminar, on 2023-01-19.

Others:

I have been learning to play carillon with Lisa Lonie, the carillonist 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 while I was in Peking University. Here is a version of the traditional piece 《高人一头的人》 (One-Upper) that Yinbo Wang and I performed in 2019.