cmengca23

Cheng Meng's Homepage


Cheng Meng

Yau Mathematical Sciences Center, Tsinghua University
Office: Shuangqing Building A, 743
Yau Mathematical Sciences Center, Tsinghua University, Beijing, China 100084
Email: cmengca95 at outlook.com, cheng319000 at mail.tsinghua.edu.cn

About Me

I am a postdoctoral fellow at Yau Mathematical Sciences Center from Fall 2024. I received my PhD from Purdue in December 2023. My advisors are Giulio Caviglia and Linquan Ma. My research interests are in commutative algebra and its interactions with algebraic geometry, homological algebra and combinatorics.

I worked on various problems in commutative algebra involving graded rings and modules, Grobner basis, homological invariants, multiplicity and characteristic p methods. My most recent work proves that the Hilbert-Kunz multiplicity of Fermat quadrics decreases as the characteristic increases. The proof relies on the modular representation theory of cyclic p-groups and provides an explicit closed formula for the multiplicity as a function of both the characteristic and the dimension. In another recent work, I investigated the dimensions of the non‑projective summands in tensor powers of modular representations of finite p-groups. When the exponent varies, I have shown that the resulting dimension sequence can have a transcendental generating function, and I have given an algorithm to compute such generating functions in the Omega-algebraic case.

Recently I am looking into the following problems:

  • Representation of commutative Artinian algebras;
  • Computations on Grobner basis.
    • I am also interested in linkages, Rees algebras in characteristic p and other problems on F-singularities.

    Publications and preprints

    11.Hilbert-Kunz multiplicity of quadrics decreases. Arxiv

    10.Asymptotic behavior of modular representations over abelian p-groups. Arxiv

    9.Finiteness and infiniteness of gradings of Noetherian rings. Arxiv

    8.Explicit Stillman bounds for all degrees (with Giulio Caviglia and Yihui Liang). Arxiv

    7.Limits of F-invariants and Riemann-Stieltjes integral. Arxiv

    6.Asymptotic colengths for families of ideals: an analytic approach (with Sudipta Das). link Arxiv

    5.h-function, Hilbert-Kunz density function and Frobenius-Poincaré function (with Alapan Mukhopadhyay). Arxiv

    4.Strongly Lech-independent ideals and Lech's conjecture, Accepted by Trans. Am. Math. Soc. link Arxiv

    3.Local cohomology tables of sequentially almost Cohen-Macaulay modules, J. Algebra 665 (2025), 596–627. link Arxiv

    2.Restrictions on Hilbert coefficients give the depth of a prime ideal inside the polynomial ring link Arxiv

    1.G-graded irreducibility and the index of reducibility, Comm. Algebra 48 (2020), no. 2, 826–832. link Arxiv

    Teaching

  • Teaching assistant for Algebra II, Spring 2026.
  • Teaching assistant for Algebra I, Fall 2025.
  • Teaching assistant for Commutative Algebra, Spring 2025.
  • Teaching assistant for Algebra I, Fall 2024.
  • Recitation instructor for MA 261, Fall 2023.
  • Recitation instructor for MA 165, Fall 2019. There is a link on this course.
    • I have been the grader for:
  • MA 546 and MA 558, Fall 2022.
  • MA 553 and MA 558, Spring 2021.
  • MA 553, MA 557 and MA 304, Fall 2020.
  • MA 553 and MA 558, Spring 2020.
  • MA 453 and MA 546, Spring 2019.
  • MA 450 and MA 553, Fall 2018.
  • MA 453, Spring 2018.
  • MA 527, Fall 2017.
  • MA 303, Spring 2017.
  • MA 304, Fall 2016.

    • Other activities

    Commutative Algebra Student Seminar

    In Spring 2022 I organized a commutative algebra student seminar. For more information about the seminar, please see here.

    ICTP Summer School

    In Summer 2022 I was a tutor in the ICTP summer school "Graduate Course on Tight Closure of Ideals and its Applications"

    Links

    My CV
    My photo

    This page was last updated on Jul 25, 2026.