Vincenzo MICALE

Assistant Professor of Algebra [MAT/02]

Vincenzo Micale, born in 1974, is a confirmed researcher of Algebra at the University of Catania since 2006. He teaches in the degree course in Mathematics and Mathematics Magistrale. He carries out research in the sector of Commutative Algebra. He was a visiting researcher at Stockholm University in Sweden and at the Universitat Autonoma de Barcelona in Spain.

Studies and Education:
- July 1997: degree in Mathematics (supervisor: prof. R. Strano) thesis entitled: " Chiusura stretta di un ideale"; mark: 110/110 with honours;
- from 1997-98 to 2001-02: PhD in Matematics at Catania University, positively accomplished with a thesis entitled: "On Analytically Unramified One-dimensional Local Rings and their Value Semigroups ";
- January 2000 - July 2001, October 2002 - July 2003 and November 2004 - March 2005: visiting scholar at Stockholm University (Sweden) with research activities under the direction of Professor Ralf Froberg;
- January - May 2004: visiting scholar at Universitat de Barcelona (Spain) with research activities under the direction of Professor S. Zarzuela;

Partecipation to the following schools:
- August 1999: " Summerschool on Computational Algebra ", Nordfjorded - Norway;
- May 2004 “School on Commutative Algebra and interactions with Algebraic Geometry and Combinatorics” Trieste.

Education grants and titles:
- 1993-95: grants for undergraduates provided by the University of Catania;
- 1997: winner of a position as PhD student in Mathematics (XIII cycle) at the University of Catania;
- 2001: national final discussion of the PhD thesis with a positive result;
- March 2006: winner of a competition for a position as a researcher in Algebra at the University of Catania;
- November 2006: come on duty as a researcher of Algebra at the Faculty of Sciences of the University of Catania;
- November 2009: confirmed as researcher of Algebra;
- Since 2006 referee for some journals; in particular, for “Communications in Algebra” and “Semigroup Forum”;


Teaching activities:
- Course for the Degree in Mathematics: Complement in Algebra;
- Course for the Master degree in Mathematics: Istitution of Algebra (second module);
- Course for the Degree in Mathematics: Support in Algebra;
- Supervisor of several first-level thesis in Mathematics, of several Master Degrees in Mathematics;

Communications at conferences:
- May 2002: Giornate di Geometria Algebrica ed argomenti correlati VI - Anacapri (Italy); communication entitled “Semigruppi Monomiali”;
- September 2003: Workshop on Commutative Algebra with applications in Geometry and Combinatorics - Piraino (Italy); communication entitled “La serie di Poincaré del modulo delle derivate di Anelli monomiali”;
- May 2005: Antalya Algebra days – Antalya (Turkey); communication entitled “The Poincaré series of the module of derivations of some monomial rings”;
- July 2007: Homological and combinatorial aspects in commutative algebra – Busteni (Romania); communication entitled “On the Buchbaumness of the associated graded ring of a numerical semigroup ring”;
- June 2009: Topics in Algebra – Stockholm (Sweden); communication entitled “On the Buchbaumness of the associated graded ring of a numerical semigroup ring”;
- February 2010: Iberian meeting on numerical semigroups - Granada (Spain); communication entitled “Apery set of a numerical semigroup and properties of the associated graded ring of a numerical semigroup ring”;
- July 2012: Iberian meeting on numerical semigroups - Vila Real (Portugal); communication entitled “ On the Betti numbers of some semigroup rings”;
- September 2014: Organizer of the INdAM meeting "International meeting on numerical semigroups" - Cortona;
- June 2015 Mega – Trento (Italy); communication entitled “Bases of subalgebras of K[[x]] and K[x]";
- July 2016 Organizer of the CIRM meeting "International meeting on numerical semigroups with applications" - Levico Terme.
- June 2017 Research Days in Commutative Algebra and Combinatorics – Messina (Italy); communication entitled “Good semigroups".

- September 2018: Organizer of the INdAM meeting "International meeting on numerical semigroups" - Cortona.

- June 2022: Organizer of the meeting INdAM workshop: International meeting on numerical semigroups - Rome.

Date 22/08/2018

Publications:

-  Micale V (2002).On monomial semigroups.  COMM. ALGEBRA 30, no. 10, 4687–4698.

-  Micale V, Molica G, Torrisi B (2002). Order bases of subalgebras of k[[X]]. COMMUTATIVE RINGS193–199, Nova Sci. Publ., Hauppauge, NY.

Micale V (2003). Order bases of subalgebras of power series rings. COMM. ALGEBRA, no. 3, 1359–1375.

- D'Anna M, Micale V (2003). Construction of one-dimensional rings with fixed value of t(R)λR(R/C)−λR(R¯/R). INT. J. COMMUT. RINGS , no.1, 23–38.

- Froberg R, Micale V (2004). The Poincaré series of the module of derivations of affine monomial curves. J. ALGEBRA 280, no. 1, 120–131.

- D'Anna M, Micale V (2006). Construction of one-dimensional rings with fixed value of t(R)λR(R/C)−λR(R¯/R). FOCUS ON COMMUTATIVE RINGS RESEARCH23–38, Nova Sci. Publ., New York.

- Micale V (2008). The Poincaré series of the module of derivations of some monomial rings. MATH. SCAND. 102, no. 1, 5–16.

 - Bertone C, Micale V (2008) On the dimension of the minimal vertex cover semigroup ring of an unmixed bipartite graph. MATEMATICHE (Catania) 63, no.2, 157–163.

- D'Anna M, Mezzasalma M, Micale V (2009). On the Buchsbaumness of the associated graded ring of a one-dimensional local ring. COMM. ALGEBRA 37, no. 5,1594–1603.

- D'Anna M, Micale V, Sammartano A (2011). On the associated graded ring of a semigroup ring. JOURNAL OF COMMUTATIVE ALGEBRA, vol. 3, p. 147-168.

- Micale V, Olteanu A (2012). On the Betti numbers of some semigroup rings. LE MATEMATICHE, vol. 67.

- D'Anna M, Micale V, Sammartano A (2013). When the associated graded ring of a semigroup ring is complete intersection.. JOURNAL OF PURE AND APPLIED ALGEBRA, vol. 217, p. 1007-1017.

- D'Anna M, Micale V, Sammartano A (2014). Classes of complete intersection numerical semigroups. SEMIGROUP FORUM, vol. 88, p. 453-467.

- D'Anna M, Di Marca M, Micale V (2015). On the Hilbert function of the tangent cone of a monomial curve. SEMIGROUP FORUM, vol. 91, p. 718-730.

- Assi A., García-Sánchez P., Micale V (2017). Bases of subalgebras of K[ [x] ] and K[x]. JOURNAL OF SYMBOLIC COMPUTATION, vol. 79, p. 4-22.

- D'Anna, M, Garcia Sanchez P, Micale V, Tozzo L (2018). Good semigroups of $N^n$. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, vol. 28, p. 179-206

- D'Anna M, Guerrieri L, Micale V (2020). The type of a good semigroup and the almost symmetric condition. MEDITERR. J. MATH. 17, no.1, Paper No. 28, 23pp.

- D'Anna M, Guerrieri L, Micale V (2020).  The Apéry set of a good semigroup. ADVANCES IN RINGS, MODULES AND FACTORIZATIONS, Springer Proc. Math. Stat., 321, p. 79-104.

- Guerrieri L, Maugeri N, Micale V (2021). Partition of the complement of good semigroup ideals and Apéry sets. COMM. ALGEBRA 49, no.10, p. 4136–4158.

- Guerrieri L, Maugeri N, Micale V (2023).  Properties and applications of Apéry set of good semigroups in N^d. J. Algebraic Combin. 57, no. 2, 353-383.

VIEW THE COURSES FROM THE A.Y. 2022/2023 TO THE PRESENT

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Academic Year 2019/2020


Academic Year 2018/2019


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Academic Year 2015/2016

My research deals with the study of numerical semigroups from the point of view of commutative algebra. In particular I am interested in studying the properties of the semigroup rings (local or graded) and their invariants in relation to the semigroups associated with them (and eventually to generalize the results obtained in the case of one-dimensional rings).