Ph.D. Graduate Student
Office: MATH 743
150 N. University Street
West Lafayette, IN 47907-2067
Email: cheng319 at purdue dot edu
I am a PhD student in mathematics. My advisors are Giulio Caviglia and Linquan Ma. I am on the job market this fall.
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, and have found a way to decompose the local cohomology table of almost Cohen-Macaulay modules.
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"
I have been the recitation instructor for MA 165. There is a link on this course.
I have been the grader for:
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.
- G-graded irreducibility and the index of reducibility, Communications in Algebra, DOI: 10.1080/00927872.2019.1662914 PDF
- Restrictions on Hilbert coefficients give the depth of a prime ideal inside the polynomial ring PDF
- Decomposition of local cohomology tables in dimension 3 PDF
- Strongly Lech-independent ideals and Lech's conjecture PDF
This page was last updated on September 27, 2022.