My research is in commutative algebra, combinatorics, and algebraic geometry, and it is supported by the NSF Grant DMS #2401522.
| 25. | Rational powers, invariant ideals, and the summation formula
with Sankhaneel Bisui, Sudipta Das, and Tài Huy Hà Submitted |
| 24. | Ladder determinantal varieties and their symbolic blowups
with Alessandro De Stefani, Luis Núñez-Betancourt, Lisa Seccia, and Matteo Varbaro Submitted |
| 23. | K-polynomials of multiplicity-free varieties
with Federico Castillo, Yairon Cid-Ruiz, and Fatemeh Mohammadi Submitted |
| 22. | The core of
monomial ideals
with Louiza Fouli, Claudia Polini, and Bernd Ulrich to appear in Algebra & Number Theory |
| 21. | Blowup algebras of determinantal ideals in prime characteristic
with Alessandro De Stefani and Luis Núñez-Betancourt Journal of the London Mathematical Society 110 (2024), e12969 |
| 20. | Computing multiplicity sequences
with Justin Chen and Youngsu Kim Journal of Software for Algebra and Geometry 14 (2024), 13-18 |
| 19. | Double Schubert polynomials do have saturated Newton polytopes
with Federico Castillo, Yairon Cid-Ruiz, and Fatemeh Mohammadi Forum of Mathematics, Sigma 11 (2023), e100 |
| 18. | Purity of monoids and characteristic-free splittings in semigroup rings
with Alessandro De Stefani and Luis Núñez-Betancourt Mathematische Zeitschrift 305:31 (2023) |
| 17. | Frobenius methods in combinatorics
with Alessandro De Stefani and Luis Núñez-Betancourt São Paulo Journal of Mathematical Sciences 17 (2023), 387-429 |
| 16. | Convex bodies and graded families of monomial ideals
with Yairon Cid-Ruiz Revista Matemática Iberoamericana 38 (2022), 2033-2056 |
| 15. | Mixed multiplicities of graded families of ideals
with Yairon Cid-Ruiz Journal of Algebra 590 (2022), 394-412 |
| 14. | When are multidegrees positive?
with Federico Castillo, Yairon Cid-Ruiz, Binglin Li, and Naizhen Zhang Advances in Mathematics 374 (2020), 107382 |
| 13. | Exterior powers and Tor-persistence
with Justin Lyle and Keri K. Sather-Wagstaff Journal of Pure and Applied Algebra 226 (2022), 106890 |
| 12. | Analytic spread and integral closure of integrally decomposable modules
with Carles Bivià-Ausina Nagoya Mathematical Journal 245 (2022), 166-191 |
| 11. | Symbolic analytic spread: upper bounds and applications
with Hailong Dao Journal of the Institute of Mathematics of Jussieu 20 (2021), 1969-1981 |
| 10. | Extremal growth of Betti numbers and trivial vanishing of (co)homology
with Justin Lyle Transactions of the American Mathematical Society 373 (2020), 7937-7958 |
| 9. | Splittings and symbolic powers of square-free monomial Ideals
with Luis Núñez-Betancourt International Mathematics Research Notices 2021 (2021), 2304-2320. |
| 8. | On asymptotic vanishing behavior of local cohomology
with Hailong Dao Mathematische Zeitschrift 295 (2020), 73-86 |
| 7. | Length of local cohomology of powers of ideals
with Hailong Dao Transactions of the American Mathematical Society 371 (2019), 3483-3503 |
| 6. | Lower bounds on projective levels of complexes
with Hannah Altmann, Eloísa Grifo, William Sanders, and Thanh Vu Journal of Algebra 491 (2017), 343-356 |
| 5. | On the growth of deviations
with Adam Boocher, Alessio D'Alì, Eloísa Grifo, and Alessio Sammartano Proceedings of the American Mathematical Society 144 (2016), 5049-5060 |
| 4. | Edge ideals and DG algebra resolutions
with Adam Boocher, Alessio D'Alì, Eloísa Grifo, and Alessio Sammartano Le Matematiche 70 (2015), no.1, 215-237 |
| 3. | Artin-Nagata properties, minimal multiplicities, and depth of fiber cones
Journal of Algebra 425 (2015), 423-449 |
| 2. | Multiplicities of classical varieties
with Jack Jeffries and Matteo Varbaro Proceedings of the London Mathematical Society 110 (2015), 1033-1055 |
| 1. | The j-multiplicity of monomial ideals
with Jack Jeffries Mathematical Research Letters 20 (2013), 729-744 |
| 3. | Improving Locality Sensitive Hashing by Efficiently Finding Projected Nearest Neighbors
with Omid Jafari and Parth Nagarkar 13th International Conference on Similarity Search and Applications (SISAP) 2020 |
| 2. | mmLSH: A Practical and Efficient Technique for Processing Approximate Nearest Neighbor Queries on Multimedia Data
with Omid Jafari and Parth Nagarkar 13th International Conference on Similarity Search and Applications (SISAP) 2020 |
| 1. | Efficient Bitmap-based Indexing and Retrieval of Similarity Search Image Queries
with Omid Jafari and Parth Nagarkar IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI) 2020 |
| MultiplicitySequence package in Macaulay2
with Justin Chen and Youngsu Kim Macaulay2 (certified by Journal of Software for Algebra and Geometry) |