Research

My research is in commutative algebra, combinatorics, and algebraic geometry, and it is supported by the NSF Grant DMS #2001645/2303605.


Publications

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. Blowup algebras of determinantal ideals in prime characteristic
with Alessandro De Stefani and Luis Núñez-Betancourt
Submitted
21. The core of monomial ideals
with Louiza Fouli, Claudia Polini, and Bernd Ulrich
to appear in Algebra & Number Theory
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

Computer Science:

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

Codes:

MultiplicitySequence package in Macaulay2
with Justin Chen and Youngsu Kim
Macaulay2 (certified by Journal of Software for Algebra and Geometry)

Invited Talks

  • VII Latin-American and the Caribbean Mathematics Congress, João Pessoa, Brazil, August 26, 2024.
  • Latin-American Algebra Colloquium (plenary), Pontificia Universidad Católica, Chile, July 22, 2024.
  • Bay Area Discrete Math Day, Santa Clara University, April 20, 2024.
  • Commutative Algebra Seminar, SLMath/MSRI, March 21, 2024.
  • Algebra Seminar, Auburn University, October 16, 2023.
  • ICMAM Latin America, Satellite Conference, Online, September 27, 2023.
  • Summer CAMP, University of Nebraska-Lincoln, August 9, 2023.
  • MSRI summer school Colloquium, University of Notre Dame, May 26, 2023.
  • Algebra Seminar, University of Missouri, April 17, 2023.
  • Tulane Mathematics Colloquium, Tulane University, March 30, 2023.
  • XII School of Mathematics, Federal University of Sergipe, Brazil (Online), February 14-16, 2023.
  • Algebra&Geometry seminar, University of Genova, Italy, December 21, 2022.
  • Department of Mathematical Sciences Colloquium, University of Texas at El Paso (Online), November 4, 2022.
  • AMS Sectional Meeting, University of Utah, October 23, 2022.
  • Combinatorial and Commutative Algebra Seminar, Oklahoma State University (Online), April 20, 2022.
  • 2022 Joint Mathematics Meeting, Online, April 7, 2022.
  • AMS Sectional Meeting, Online, March 26, 2022.
  • AMS Sectional Meeting, Online, March 19, 2022.
  • Southwest Local Algebra Meeting (SLAM), Baylor University, February 26, 2022.
  • School of Mathematical and Statistical Sciences Colloquium, Arizona State University, February 22, 2022.
  • Department of Mathematics Millican Colloquium, University of North Texas, February 8, 2022.
  • Department of Mathematics, Statistics, and Computer Science Colloquium, University of Ilinois Chicago (Online), December 7, 2021.
  • AG-CA Seminar, University of Notre Dame (Online), November 16, 2021.
  • Commutative Algebra Seminar, University of Illinois at Chicago (Online), November 4, 2021.
  • AMS Sectional Meeting, Online, October 23, 2021.
  • National Congress of the Mexican Math Society, Online, October 21, 2021.
  • Algebra and Algebraic Geometry Seminar, McMaster University, Canada (Online), July 19, 2021.
  • Virtual commutative algebra seminar, IIT Bombay, India (Online), July 9, 2021.
  • Fellowship of the Ring, MSRI (Online), April 29, 2021.
  • AMS Sectional Meeting, Online, April 17, 2021.
  • Department of Mathematics Colloquium, New Mexico State University (Online), April 9, 2021.
  • Algebra and Geometry Seminar, Iowa State University (Online), March 16, 2021.
  • Department of Mathematics Colloquium, University of California, Riverside (Online), February 24, 2021.
  • Combinatorics Seminar, University of Kansas (Online), November 13, 2020.
  • Department of Mathematics Colloquium, Universidad de los Andes, Colombia (Online), October 22, 2020.
  • Department of Mathematics Colloquium, University of New Mexico (Online), October 13, 2020.
  • AMS Sectional Meeting, Online, October 3, 2020.
  • AG and CA seminar, NU/UIC/UofC (Online), July 29, 2020.
  • eCARs conference, Online, June 28, 2020.
  • Algebra Seminar, Universities of Neuchatel, Fribourg, and Bern, Switzerland (Online), May 15, 2020.
  • AMS Sectional Meeting, Purdue University, April 5, 2020. (Meeting Canceled)
  • Algebra and Algebraic Geometry Seminar, University of Wisconsin, Madison, February 7, 2020.
  • Commutative Algebra Seminar, Purdue University, April 22, 2019.
  • AMS Sectional Meeting, Auburn University, March 15, 2019.
  • Frobenius Action in Commutative Algebra Workshop, Barcelona, Spain, January 18, 2019.
  • Algebra Seminar, Universitat Politècnica de València, Spain, January 15, 2019.
  • Fall School in Commutative Algebra, CIMAT, Mexico, November 13-17, 2018.
  • Algebra Seminar , Georgia State University, September 13, 2018.
  • Public Lecture at ECCO 2018, Barranquilla, Colombia, June 7, 2018.
  • Colombian-Mexican Math Societies joint meeting, Universidad del Norte, Colombia, May 30, 2018.
  • AMS Sectional Meeting, Portland State University, April 14, 2018.
  • Commutative Algebra and Algebraic Geometry Seminar, CIMAT, Mexico, March 22, 2018.
  • Geometry and Topology Seminar, San Francisco State University, March 12, 2018.
  • Commutative Algebra Seminar, University of Michigan, November 2, 2017.
  • Commutative Algebra Seminar, University of Utah, November 21, 2014; October 19, 2017.
  • PRIMA 2017, Oaxaca-Mexico, August 14, 2017.
  • Combinatorial and Commutative Algebra Seminar, Oklahoma State University, April 20, 2017.
  • Commutative Algebra Seminar, University of Nebraska-Lincoln, April 10, 2017.
  • KuMuNu jr 2017, University of Nebraska-Lincoln, April 8, 2017.
  • Algebra Seminar, University of Missouri, February 27, 2017.
  • Department of Mathematics Colloquium, New Mexico State University, February 9, 2017.
  • 2016 CMS Winter Meeting, Niagara Falls-Canada, December 3, 2016.
  • Algebra & Combinatorics Seminar, Tulane University, November 10, 2016.
  • Commutative Algebra Seminar, Purdue University, February 22, October 21, October 28, 2013; February 27, November 5, 2014; February 4, October 7, 2015; October 21, 2016.
  • KUMUNU 2016, University of Kansas, October 1, 2016.
  • AMS Sectional Meeting, North Dakota State University, April 16, 2016.
  • Algebra Seminar, University of Arkansas, January 29, 2016.
  • AMS Sectional Meeting, Rutgers University, November 14, 2015.
  • Combinatorics Seminar, University of Kansas, November 6, 2015.
  • Midwest Commutative Algebra Meeting, Purdue University, August 5, 2015.
  • Commutative Algebra and related topics 2015, University of Kansas, March 22, 2015.
  • 2015 Joint Mathematics Meeting, San Antonio, TX, January 13, 2015.
  • AMS Sectional Meeting, San Francisco State University, October 26, 2014.
  • AMS Sectional Meeting, Dalhousie University, October 19, 2014.
  • AMS Sectional Meeting, University of New Mexico, April 5, 2014.
  • Commutative Ring Theory Seminar, University of Illinois at Urbana-Champaign, March 7, October 24, 2013.
  • AMS Sectional Meeting, University of Louisville, October 5, 2013.
  • KuMuNu jr 2013, University of Nebraska-Lincoln, April 22, 2013.
  • Algebraic Geometry and Commutative Algebra Seminar, University of Notre Dame, February 26, 2013.