Research interests
My main interest is in Combinatorial Commutative Algebra. I have worked on studying the relations between Commutative Algebra and Additive Combinatorics, especially in the case of projective monomial curves and Additive Number Theory.
Publications
4. I. García-Marco, P. Gimenez, and M. González-Sánchez, “Computational Aspects of the Short Resolution”. Preprint, 2025. [preprint]
3. M. González-Sánchez, S. Singh, and H. Srinivasan, “The Betti numbers of Kunz-Waldi Semigroups”. Proc. Amer. Math. Soc., 153, 4215-4224 (2025). [preprint] [paper]
2. I. García-Marco, P. Gimenez, and M. González-Sánchez, “Projective Cohen-Macaulay monomial curves and their affine charts” Ricerche Mat. 74, 2239-2260 (2025). [preprint] [paper]
1. P. Gimenez and M. González-Sánchez, “Castelnuovo-Mumford regularity of projective monomial curves via sumsets” Mediterr. J. Math. 20, 287 (2023). [preprint] [paper]
Software Implementations
1. M. González-Sánchez, “ShortRes: A Sage package to compute the short resolution of a weighted homogeneous ideal” GitHub repository, 2025. https://github.com/mgonzalezsanchez/shortRes
Research stays
University of Missouri-Columbia, under the supervision of Hema Srinivasan. September-December 2024
Universidad de La Laguna, under the supervision of Ignacio García-Marco. June 13-23, 2024
Universiad de La Laguna, under the supervision of Ignacio García-Marco. May 9-23, 2023
(Selection of ) Talks
RSME 2025 (Bilbao, Spain). Computational aspects of the short resolution. January 13-17, 2025
Algebra Seminar (University of Missouri-Columbia, USA). Projective vs. affine monomial curves: equality of their Betti numbers. October 21, 2024
Algebra Seminar (University of Missouri-Columbia, USA). Additive number theory meets commutative algebra. October 14, 2024
MEGA2024 (Leipzig, Germany). Projective Cohen-Macaulay monomial curves and their affine projections. July 29 - August 2, 2024
RSME·24 (Pamplona, Spain). Castelnuovo-Mumford regularity of projective monomial curves, sumsets and semigroups. January 22-26, 2024
ACA2023 (Warsaw, Poland). Sumsets and the Castelnuovo-Mumford regularity of projective monomial curves. July 17-21, 2023