My research focuses on arithmetic algebraic geometry and number theory, particularly geometric ramification theory and motivic cohomology.
Keyword: Characteristic class; Characteristic cycle; Singular support; Milnor formula; Bloch conductor formula; Non-acyclicity class; Motivic cohomology
Publications and Preprints
- Cohomological Milnor formula and Saito's conjecture on characteristic classes (with Yigeng Zhao), Inventiones Mathematicae 240 (2025) : 123-191. (Here is the ArXiv version)
For the fibration formula (Theorem 5.1), here is an alternative proof based on a more concise idea suggested by an anonymous referee. We thank him/her very much. PDF
On Swan classes of contructible sheaves (with Yigeng Zhao)
- Characteristic cycles and non-acyclicity classes for constructible etale sheaves (with Jiangnan Xiong), PDF
- The quadratic Artin conductor of a motivic spectrum (with Fangzhou Jin), ArXiv
- The pro-Chern-Schwarz-MacPherson class in Borel-Moore motivic homology (with Fangzhou Jin and Peng Sun), ArXiv
- Kunneth formulas for motives and additivity of traces (with Fangzhou Jin).
Advances in Mathematics 376 (2021) 107446，83 pages.
- Characteristic class and the ε-factor of an etale sheaf (with Naoya Umezaki and Yigeng Zhao),
Trans.Amer.Math.Soc. 373 (2020):6887-6927.
- On the Relative Twist Formula of ℓ-adic Sheaves (with Yigeng Zhao),
Acta Mathematica Sinica, 2021, Vol.37, No.1, pp.73-94.
- Motivic singular support (with Denis-Charles Cisinski), preprint.
- Relative singular support and the semi-continuity of characteristic cycles for etale sheaves (with Haoyu Hu), Selecta Mathematica, Volume 24,Issue 3,(2018):2235-2273. PDF
- Semi-continuity for total dimension divisors of etale sheaves (with Haoyu Hu), International Journal of Mathematics, Volume 28, Issue 01, 2017. PDF
- Logarithmic version of the Milnor formula, Asian Journal of Mathematics, Volume 21, No. 3 (2017). PDF
- Logarithmic version of the Milnor formula (research announcement), RIMS Kokyuroku Bessatsu B64 (2017), 195-199. PDF (This is a conference publication)
- Derivatives of Siegel modular forms and modular connections, Manuscripta Mathematica, January 2015, Volume 146, Issue 1, pp 65–84(with Linsheng Yin). PDF
- On the GL(r)×GL(r+s) ×GL(s) convolution, Journal of Number Theory 134, 2014:130-141(with Li Sun). PDF
Grants（招募博后，欢迎邮件咨询！！！）
- NSFC general program 12271006, 2023-2026, Quadratic invariants in geometric ramification.
- National Key R&D Program 2021YFA1001400, 2022-2026, L-functions and characteristic classes of varieties.
- NSFC young scientists fund 11901008, 2020-2022, On the ramified twist formula for epsilon factors of l-adic sheaves.
Lecture Notes
- Research statement: Geometric Ramification Theory.
- Quadratic conductor formula/Milnor formula for motivic spectra. PDF
- Non-acyclicity classes. PDF1 ...PDF2 .......handWriting PDF
- Talks on the epsilon factors of l-adic etale sheaves. Jussieu SFB
- A blow up formula for Gysin pull-back. PDF (Appendix to the paper: Characteristic class and the epsilon factor of an etale sheaf)