News
Advising and Mentoring
Mentoring is a fundamental part of my academic career. These are the students who have completed at least one research paper under my supervision: Leo Abedi, Anay Aggarwal, Cecilia Aguilera, Khalid Ajran, Sofia Albizu-Campos, Aaryan Arora, Aaditya Bilakanti, Grant Blitz, Juliet Bringas, Alan Bu, Olivia Chen, Timothy Chen, Jiya Dani, Anna Deng, Jonathan Du, Victor Gonzalez, Omar Graia, Andre Hamelberg, Darren Han, Leo Hong, Joshua Jang, Henry Jiang, Nancy Jiang, Amrit Kandasamy, Shihan Kanungo, Harry Kim, Bangzheng Li, Bryan Li, Eddy Li, Evin Liang, Hengrui Liang, Andrew Lin, Jonathan Liu, Susie Lu, Tony Lu, Jason Mao, Skyler Mao, Arav Paladiya, Ishan Panpaliya, Harold Polo, Henrick Rabinovitz, Pedro Rodríguez, Shimon Schlessinger, Easton Singer, Marcos Tirador, Joseph Vulakh, Alexander Wang, Elena Whitford, Jessica Wu, Jason Yang, Alan Yao, Jason Zeng, Qiao (Tiger) Zhang, Shaohuan Zhang, Alex Zhao, Lerchen Zhong, and Sophie Zhu.
Also, these are my graduate and undergraduate advisees.
- Harold Polo
Title: Arithmetic of Polynomial-Like Semidomains
PhD Dissertation, 2023. - Pedro A. Rodríguez
Current PhD student at Clemson University.
Title: Subatomicity in Lattice Monoids
Undergraduate Thesis, 2023. - Juliet Bringas
Title: On the Atomic Structure and Factorizations of Generalized Rational Cyclic Semirings
Undergraduate Thesis, 2024. - Marcos Tirador
Title: On the Atomicity of Power Monoids of Puiseux Monoids
Undergraduate Thesis, 2024.
MIT PRIMES
I have been a research mentor for MIT PRIMES since 2021. Here are the papers my PRIMES students have produced under my supervision, by PRIMES year.
PRIMES 2021
On the primality and elasticity of algebraic valuations of cyclic free semirings
by Nancy Jiang, Bangzheng Li, and Sophie Zhu
International Journal of Algebra and Computation, Vol. 33 (2023) 197–210.Divisibility in rings of integer-valued polynomials
by Bangzheng Li (with F. Gotti)
New York Journal of Mathematics, Vol. 28 (2022) 117–139.Factorizations in evaluation monoids of Laurent semirings
by Sophie Zhu
Communications in Algebra, Vol. 50 (2022) 2719–2730.Atomic semigroup rings and the ascending chain condition on principal ideals
by Bangzheng Li (with F. Gotti)
Proceedings of the American Mathematical Society, Vol. 151 (2023) 2291–2302.Divisibility and a weak ascending chain condition on principal ideals
by Bangzheng Li (with F. Gotti)
Preprint on arXiv.
PRIMES 2022
Length-factoriality and pure irreducibility
by Alan Bu, Joseph Vulakh, and Alex Zhao
Communications in Algebra, Vol. 51 (2023) 3745–3755.On the atomic structure of torsion-free monoids
by Joseph Vulakh (with F. Gotti)
Semigroup Forum, Vol. 107 (2023) 402–423.One-dimensional monoid algebras and ascending chains of principal ideals
by Alan Bu and Alex Zhao (with F. Gotti and B. Li)
European Journal of Mathematics, Vol. 12 (2026) 57.
PRIMES 2023
Betti graphs and atomization of Puiseux monoids
by Joshua Jang, Jason Mao, and Skyler Mao (with S. T. Chapman)
Bulletin of the Australian Mathematical Society, Vol. 111 (2025) 80–92.A weaker notion of the finite factorization property
by Henry Jiang, Shihan Kanungo, and Harry Kim
Communications of the Korean Mathematical Society, Vol. 39 (2024) 313–329.The Furstenberg property in Puiseux monoids
by Andrew Lin, Henrick Rabinovitz, and Qiao (Tiger) Zhang
Preprint on arXiv.On the ascent of atomicity to monoid algebras
by Henrick Rabinovitz (with F. Gotti)
Journal of Algebra, Vol. 663 (2025) 857–881.
PRIMES 2024
On the internal sum of Puiseux monoids
by Jonathan Du, Bryan Li, and Shaohuan Zhang
Korean Journal of Mathematics, Vol. 32 (2024) 745–757.On finitary power monoids of linearly orderable monoids
by Jiya Dani, Leo Hong, and Shimon Schlessinger (with B. Li and F. Gotti)
Preprint on arXiv.On maximal common divisors in Puiseux monoids
by Evin Liang, Alexander Wang, and Lerchen Zhong
Preprint on arXiv.
PRIMES 2025
Maximal common divisors in monoid algebras
by Grant Blitz, Darren Han, and Hengrui Liang (with F. Gotti)
Preprint on arXiv.On the additive structure of algebraic valuations of polynomial semirings II
by Timothy Chen, Tony Lu, and Alan Yao (with F. Gotti)
Preprint on arXiv.An unrestricted notion of the finite factorization property
by Jonathan Du (with F. Gotti)
Preprint on arXiv.
CrowdMath
I am currently the Lead Mentor of CrowdMath (since 2022), a free year-long online research program in mathematics, which is open to all high-schoolers and undergrads around the world. Feel free to sign up or get in touch with me if you have any questions. Here are the papers produced in CrowdMath since 2022. The project page of CrowdMath 2023 is here.
Factorization in additive monoids of evaluation polynomial semirings
by Khalid Ajran, Juliet Bringas, Bangzheng Li, Easton Singer, and Marcos Tirador
Communications in Algebra, Vol. 51 (2023) 4347–4362.On the atomicity of power monoids of Puiseux monoids
by Victor Gonzalez, Eddy Li, Henrick Rabinovitz, Pedro Rodríguez, and Marcos Tirador
International Journal of Algebra and Computation, Vol. 35 (2025) 167–181.On the ascent of almost and quasi-atomicity to monoid semidomains
by Victor Gonzalez and Ishan Panpaliya (with F. Gotti)
Journal of Commutative Algebra (to appear).On primality and atomicity of numerical power monoids
by Anay Aggarwal and Susie Lu (with F. Gotti)
Preprint on arXiv.On GL-domains and the ascent of the IDF-property
by Victor Gonzalez and Ishan Panpaliya
Preprint on arXiv.On near atomicity and a characterization of the FF property
by Jonathan Du and Leo Hong (with F. Gotti)
Preprint on arXiv.The Bi-UF Positive Conjecture for quadratic monogenic semirings and related progress
by Omar Graia, Darren Han, and Hengrui Liang (with F. Gotti)
Preprint on arXiv.
CrowdMath Internship (CMI)
Here are the papers produced by the research groups I have mentored in the CrowdMath Internship.
CMI 2025 (Spring Term)
On the set of atoms and strong atoms in additive monoids of cyclic semidomains
by Jiya Dani, Anna Deng, Bryan Li, Arav Paladiya, and Jason Zeng (with M. Gotti and J. Vulakh)
Communications in Algebra (2026).Factorizations in rational monogenic semidomains
by Anna Deng and Jason Zeng (with F. Gotti)
Preprint on arXiv.Factorizations in algebraic monogenic semidomains
by Jiya Dani, Bryan Li, and Arav Paladiya (with F. Gotti)
Preprint on arXiv.
CMI 2025 (Fall Term)
- On the additive monoids of finitely generated rational semirings
by Leo Abedi, Aaryan Arora, Olivia Chen, Elena Whitford, and Jessica Wu (with M. Gotti)
Preprint.
CMI 2026 (Year-Long)
- The Bi-UFS Positive Conjecture for algebraic semidomains
by Aaditya Bilakanti, Amrit Kandasamy, Hengrui Liang, Jonathan Liu, Jason Yang, and Alan Yao (with M. Gotti and H. Polo)
Preprint on arXiv.
Further Publications I Have Supervised
On the set of lengths of Puiseux monoids generated by multiple geometric sequences
by Harold Polo
Communications of the Korean Mathematical Society, Vol. 35 (2020) 1057–1073.On the atomic structure of exponential Puiseux monoids and semirings
by Sofia Albizu-Campos, Juliet Bringas, and Harold Polo
Communications in Algebra, Vol. 49 (2021) 850–863.Approximating length-based invariants in atomic Puiseux monoids
by Harold Polo
Algebra and Discrete Mathematics, Vol. 33 (2022) 128–139.On the set of molecules of numerical and Puiseux monoids
by Marcos Tirador (with M. Gotti)
In: Rings, Monoids, and Module Theory (Eds. A. Badawi and J. Coykendall) Springer Proceedings in Mathematics and Statistics, Vol. 382, Singapore, 2022.Factorization invariants of the additive structure of exponential Puiseux semirings
by Harold Polo
Journal of Algebra and Its Applications, Vol. 22 (2023) 2350077.Subatomicity in rank-2 lattice monoids
by Pedro Rodríguez and Marcos Tirador (with C. Liu)
Journal of Commutative Algebra, Vol. 16 (2024) 337–352.
Awards Earned by my Students
- Jonathan Du
- 2026 Regeneron STS: 9th Place
- Jason Mao
- 2024 Regeneron ISEF: Mu Alpha Theta Second Award
- Shihan Kanungo
- 2023 Spirit of Ramanujan: SOR Fellow
- Joseph Vulakh
- 2023 Regeneron ISEF: 3rd Special Award (from AMS)
- Sophie Zhu
- 2023 Regeneron STS: Finalist
- Sophie Zhu
- 2022 Regeneron ISEF: 4th Grand Award
- 2022 Regeneron ISEF: 2nd Special Award (from AMS)
- Bangzheng Li
- 2022 Regeneron STS: Scholar