Research team:

• Lect. Dr. Dumitru I. Stamate (project director), University of Bucharest, CV
• Conf. Dr. Mircea Cimpoeas, Universitatea Politehnica din Bucuresti & IMAR, CV
• C.S. Dr. Rodica Dinu, "Simion Stoilow" Institute of Mathematics of the Romanian Academy (IMAR), CV
• Asist. Dr. Claudia Ciobanu, Universitatea Politehnica din Bucuresti, CV
• Gabriela Petcu, University of Bucharest, master student, CV. [hired since 1 August 2022]
• Ph.D. student, vacant position

Description of the project:
In this project we consider problems in commutative algebra related to Groebner bases, deformations, free resolutions and the persistence of the invariants through deformations, and also new extensions of the Gorenstein property. On one hand, we aim to extend the theoretical framework, and on the other hand we have in mind applications to classes of combinatorially defined algebras.

Publications and preprints:

1. Dumitru I. Stamate, On the occurrence of complete intersections in shifted families of numerical semigroups, Research in the Mathematical Sciences vol 9 (2022), Article number: 32 (5 pp). DOI 10.1007/s40687-022-00328-0. Preprint version.
2. Rodica Dinu, Francesco Navarra, Non-simple polyominoes of Konig type, preprint 2022, submitted. 15pp. Preprint version available at arXiv:2210.12665 [math.AC].
3. Mircea Cimpoeas, On a generalization of monomial groups, Monatshefte fur Mathematik, 2022, available online. DOI 10.1007/s00605-022-01762-6.
4. Mircea Cimpoeas, Alexandru F. Radu, On supercharacter theoretic generalizations of monomial groups and Artin's conjecture, Czechoslovak Mathematical Journal Vol. 72 (2022), No. 4, pp. 1065-1079. DOI 10.21136/CMJ.2022.0352-21.
5. Mircea Cimpoeas, Alexandru F. Radu, On the monoid algebra associated to the monomial characters of a finite group, 2022, to appear in Quaestiones Mathematicae, 14 pp. Preprint version available at arXiv:2205.13597 [math.RT].

Scientific reports:

• 2022: [pdf]

Research stages abroad funded by the grant:

2022:
• Rodica Dinu at the University of Duisburg-Essen, Campus Essen, Germany, June 2022 (2 weeks). Host: Prof. Juergen Herzog,
• Gabriela Petcu attended the EMS Summer School on Combinatorial Commutative Algebra, Gebze Technical University, Turkey, 8-12 August 2022.
• Dumitru Stamate at the University of Duisburg-Essen, Campus Essen, Germany, September 2022 (2 weeks). Host: Prof. Juergen Herzog.

Invited specialists :

• Alexandra Seceleanu from the University of Nebraska, Lincoln, USA visited between 16-19 July 2022. She also gave one lecture on Symmetric shifted monomial ideals in the Commutative Algebra Seminar at the Faculty of Mathematics and Computer Science, University of Bucharest.

Dissemination of the results. Conference and seminar talks:

1. Dumitru Stamate, Ulrich elements in normal affine semigroup rings, Algebra Seminar, University of Pisa, 17 May 2022.
2. Dumitru Stamate, Ulrich elements in normal affine semigroup rings, INdAM Workshop: International Meeting on Numerical Semigroups 2022, Rome, Italy, 13-17 June 2022.
3. Mircea Cimpoeas, A note on the monomial characters of a wreath product of groups, C.A.I.M. 29th edition, Universitatea de stat din Tiraspol, 25-28 August 2022, Chisinau, Republic of Moldova.
4. Mircea Cimpoeas, Almost monomial groups, Yearly Conference of SSMR, the Romanian Mathematical Society, Universitatea Politehnica din Bucuresti, 22 October 2022, Bucharest, Romania.
5. Dumitru Stamate, On the occurrence of complete intersections in shifted families of numerical semigroups, FMI-IMAR Commutative Algebra Seminar, 8 nov 2022.
6. Mircea Cimpoeas, On the monomial algebra associated to the monomial characters of a finite group, FMI-IMAR Commutative Algebra Seminar, 15 nov 2022.

Events organized:

• The 11th edition of the Workshop for Young Researchers in Mathematics, 19-20 May 2022, IMAR, Bucharest (hybrid), was co-organized by Cristina Anghel, Rodica Dinu, Alexandra Melnig and Remus Radu. R. Dinu and C. Anghel co-organized the Algebra, Geometry, Number Theory & Topology Section.
• Dumitru Stamate was part of the scientific committee for the EMS Summer School on Combinatorial Commutative Algebra, Gebze Technical University, Turkey, 8-12 August 2022, together with Fatemeh Mohammadi and Mufit Sezer.