cmengca23

Cheng Meng

Yau Mathematical Sciences Center, Tsinghua University
Office: Shuangqing Building A, 743
Yau Mathematical Sciences Center, Tsinghua University, Beijing, China 100084
Email: cheng319 at purdue dot edu(expired), cmengca95 at outlook.com, cheng319000 at mail.tsinghua.edu.cn

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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 problems regarding the graded-irreducibility of graded modules, generic initial ideals, Boij-Soderberg theory for local cohomology tables, Lech's conjecture on multiplicities of flat local extension of Noetherian local rings, and singularities in prime characteristic. I have proved a new case of Lech's conjecture, found a way to decompose the local cohomology table of almost Cohen-Macaulay modules, and have developed a new invariant of local rings of characteristic p called h-function, which is related to the Hilbert-Kunz multiplicity, the F-signature and the F-thresholds of rings.

Recently I am working on the following problems:

Explicit computation of Hilbert-Kunz multiplicity, via the h-function;

Asymptotic lengths of families of ideals;

Stillman type bound, which bounds the homological data of ideals with bounded number of generators and generating degrees.

I am also looking into problems related to linkage and set-theoretic complete intersections.

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"

Teaching

Past

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.

Publications

• G-graded irreducibility and the index of reducibility, Communications in Algebra, DOI: 10.1080/00927872.2019.1662914 PDF Arxiv

Preprints

• Restrictions on Hilbert coefficients give the depth of a prime ideal inside the polynomial ring PDF

• Local cohomology tables of sequentially almost Cohen-Macaulay modules (accepted by Journal of Algebra) PDF Arxiv

• Strongly Lech-independent ideals and Lech's conjecture PDF Arxiv

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

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

Links

My CV
My photo

This page was last updated on Dec 8, 2024. </li></ul>