Luís Duarte
My name is Luís Duarte and I am currently a posdoc student at Stockholm University under a Sverker Lerheden scholarship.
Before that I was a posdoc student for a year at the University of Genova, in Italy, where I also did my PhD. My advisors were Maria Evelina Rossi and Alessandro De Stefani.
Before that, I did my bachelor's and master's degrees at Instituto Superior Técnico, Lisbon, where I was introduced to commutative algebra by professor Maria Vaz Pinto.
Publications and preprints
My research interest is in commutative algebra. Most of my work up to date is related to the study of small perturbations of ideals in local rings. Besides that, I am also interested in problems in homological algebra, either related to local cohomology or infinite resolutions.
Local cohomology under small perturbations, to appear in Nagoya Mathematical Journal (arXiv)
Betti numbers under small perturbations - Journal of Algebra, Vol. 594, 2022, p. 138-153 (arXiv)
Bimodules of Banach space nest algebras (with Lina Oliveira) - The Quarterly Journal of Mathematics, Vol. 73, Issue 1, 2022, p. 213-237 (arXiv)
Invited talks
04-2024 - Algebra and geometry seminar, University of Stockholm.
12/2023 - Online seminar at the University of Stockholm.
05/2023 - I gave a short talk at the "School on Commutative Algebra and Algebraic Geometry in Prime Characteristics" at ICTP, Trieste, Italy.
02/2023 - IIT Bombay Virtual Commutative Algebra Seminar.
01/2023 - Invited speaker at the conference "Written Geometry: Commutative Algebra" at CIRM, Luminy, France.
04/2022 - Algebra and geometry seminar, University of Genova.
03/2022 - Special Session in Combinatorial Techniques in Commutative Algebra, AMS meeting at Purdue University.
03/2022 - Commutative algebra seminar, University of Nebraska.
03/2022 - Algebraic geometry and commutative algebra seminar, University of Notre Dame.
02/2022 - Commutative algebra seminar, Purdue University.
Participations at schools and conferences
05-06/2024 - I will be participating in the preparatory school and the conference on 'Lefschetz properties in algebra, geometry, topology and combinatorics' in Krakow, Poland.
06/2023 - I participated in the the P.R.A.G.Mat.I.C Research school in Algebraic Geometry and Commutative Algebra in Catania, Italy.
05/2023 - I attended the "School and Workshop on Commutative Algebra and Algebraic Geometry in Prime Characteristics" at ICTP, Trieste, Italy.
02/2023 - I was invited to attend the workshop "Resolutions in Local Algebra and Singularity Theory" at Oberwolfach, Germany.
01/2023 - I was invited to attend the conference "Written Geometry: Commutative Algebra" at CIRM, Luminy, France.
12/2022 - I will be atending the AGATES workshop in "Deformation theory" in Warsaw, Poland.
08/2022 - I participated in the workshop "Local cohomology and related topics" in Stockholm, Sweden.
06/2022 - I participated in the conference "75+80=155 years of commutative algebra" in Osnabrück, Germany.
05 - 07/2022 - I was selected to participate in the online school "Graduate course on tight closure of ideals and its applications".
Research visits
02-03/2022 - Purdue University. I was a visiting student there for 2 months.
03/2022 - Notre Dame University.
03/2022 - University of Nebraska.