Lucia Maria MARINO

Education

University of Catania, Italy

• Ph. D. in Mathematics awarded in June 2002.

Thesis Title: On conductor degrees for 0-dimensional schemes.

Supervisor : A. Ragusa

Date: October 18, 2018

• M.Sc. in Mathematics, University of Catania, Italy, 1996
Thesis Title: Limitazioni 
sui numeri di Betti graduati

Supervisor: A. Ragusa

 

Area of Research

My predominant area of research is Combinatorics with a primary emphasis on Combinatorial Design Theory and Graph Theory.

Another research field is algebraic geometry. In particular zero-dimensional schemes in P1 × P1, Hilbert functions and minimal free resolutions.

 

Current position

From January 2022 Associate Professor in  Geometry at the Mathematics and Computer Science Department of the University of Catania.

 

Abilitation

 

National Academics Qualification as Associate Professor in Algebra and Geometria, 01/A2

(sector MAT03, geometry), from July 31^st, 2017 to July 31 st, 2023.

 

Teaching Experience

 

• Teaching Assistant Department of Mathematics and Computer Sciences. Course: Combinatorial Geometry

• Assist. Prof.: Department of Electrical, Electronics and Computer Engineering (DIEEI) - and Department of Civil Engineering and Architecture (DICAR  University of Catania- Italy (October 2007 – present)

Course: Linear Algebra and Geometry for Engineers.

• Teaching assistant at Faculty of Engineering, University of Catania. (November 2006 - October 2007)

Course: Linear Algebra and Geometry for Engineers.

• Instructor at Faculty of Engineering, University of Catania (November 2001-October 2004)

 

Past position

 

• Postdoctoral research fellow for two years, Faculty of engineering of Catania, Italy (2005-2007)

• Visitor at the University of Berkely, California (USA) for six months. (2005)

• Fellowship, Department of Mathematics in Tucson, University of Arizona (USA) for six months with support of the University of Catania. (2003)

• Postdoctoral research fellow for two years, supported by Department of Mathematics in Catania (2002-2004)

 

 

Research Projects

• Member of “Progetto GNSAGA - INDAM: Numeri di Betti di Algebre graduate.” - Coord. Prof. A. Ragusa. Sedi: Catania - Messina- Reggio Calabria.

• PRIN 2003 Member of the Research Project"Algebra commutativa e computazionale" - Coord. scient. Valla G., Resp. scient.: Strano R. Univ. di CATANIA.

• PRIN 2005 Member of the Research Project-"Algebra commutativa, combinatoria e computazionale" - Coord. scient. Valla G., Resp. scient. Strano R. Univ. di CATANIA.

• PRIN 2007 Member of the Research Project "Algebra Commutativa e Combinatorica con applicazioni alla Geometria Algebrica" - Coord. scient. Valla G., Resp. scient. Ragusa A. Univ. di CATANIA.

• PRA 2007, 2008, 2009, 2010,2011 Member of PROGETTO DI RICERCA FINANZIABILE CON FONDI DI ATENEO, Resp. Scient.: Ragusa A. Title of the project: Metodi algebrici, omologici e computazionali nello studio delle varietà algebriche.

• PRIN 2011 Member of the Research Project "Geometria delle Varietà algebriche" - Coord. scient. A. Verra., Resp. scient. F. Russo Univ. di CATANIA

• Anno 2012 - Ripartizione risorse destinate al finanziamento dei ricercatori

• FIR 2014 Member of the Research Project “Block designs and Graph designs- their Applications" - Principal Investigator Gionfriddo Mario dell' Università di Catania

• 2016- 18 Member of the Reaserch Project “New Trends in Geometry, Topology and Combinatorics” Resp. scient. E. Guardo, Univ. of Catania.

• 2018 FABR: admitted to financing by ANVUR, email: finanziamenti_ricerca@anvur.it

 

 

 

Refereeing, Review and Editorial Board

• Member of Editorial Board for Advances in Pure Mathematics since 2017, ISSN Print: 2160-0368, ISSN Online: 2160-0384

• Reviewer for Mathematical Reviews (AMS published in MathSciNet. Since 2004).

• Referee for international journals.

 

 

Research Publications

•  "Edge balanced star‐hypergraph designs and vertex colorings of path designs " in collaboration with Paola Bonacini, J Combin Des. (2022);1–18. 
• “On Voloshin colorings in 3-hypergraph designs”,  in collaboration with Paola Bonacini, Discrete Mathematics, Volume 343, Issue 10, October 2020, 112030, pubblicato online il 20 giugno 2020, https:// doi.org/10.1016/j.disc.2020.112030.
•  “Edge balanced 3-uniform hypergraph designs”,  in collaboration with Paola Bonacini and Mario Gionfriddo, Mathematics 2020, 8, 1353.
• “Blocking sets for cycles and paths designs”,  in collaboration with Paola Bonacini, Appl. Anal. Discrete Math, 14 (2020), 183–197.
•  “Perfect blocking sets in P3-designs”,  in collaboration with Paola Bonacini and Mario Gionfriddo, The Art of Discrete and Applied Mathematics, 1 (2018), #P2.08. 

• “The spectrum of balanced P^3(1,5)-designs”, in collaboration with Paola Bonacini, Maria Di Giovanni, Mario Gionfriddo, and Antoinette Tripodi, Contributions to Discrete Mathematics, 12 (1), 2017, 133-142.

• Dodecagon Quadrangle Systems having the most large spectrum, in collaboration with Mario Gionfriddo, Applied Mathematical Sciences, 10 (2016), no. 31, 1501-1508.

• On the lower and upper chromatic index of C6-systems, in collaboration with Paola Bonacini and Mario Gionfriddo, preprint.

• Equitable block colorings for 8-cycle systems, in collaboration with Paola Bonacini, The Australasian Journal of Combinatorics, 69 (2017), no. 2, 184–196

• Nonagon quadruple systems: existence, balance, embeddings, in collaboration with Paola Bonacini and Mario Gionfriddo, The Australasian Journal of Combinatorics, 66 (2016), no. 3, 393-406.

• On the spectrum of Octagon Quadrangle Systems of any index, in collaboration with Paola Bonacini, Contributions to Discrete Mathematics, 12 (1), 2017, 74-82.

• Nestings House-designs, in collaboration with Paola Bonacini and Mario Gionfriddo Discrete Mathematics, 339 (2016), n° 4, 1291-1299

• Construction of non-cyclic balanced P(3)(1,5)-designs, in collaboration with Paola Bonacini and Mario Gionfriddo, Applied Mathematical Sciences, 9 (2015), no.126, 6273-6282

• Balanced House-systems and Nestings, in collaboration with Paola Bonacini and Mario Gionfriddo, Ars Combinatoria, 121 (2015), 429-436.

• Equitable tricolourings for 4-cycle systems, in collaboration with Paola Bonacini,

Applied Mathematical Sciences, 9(2015), no.58, 2881-2887.

• Equitable block colourings, in collaboration with Paola Bonacini, Ars Combinatoria, 120 (2015), 255-258.

• Minimal free resolutions and Hilbert functions in P¹x P¹, in collaboration with Paola Bonacini, Algebra Colloquium 22 (2015), no.1, 97-108.

• Homogeneous edge-coloring of graphs , in collaboration with Paola Bonacini and Maria Grazia Cinquegrani to appear in Utilitas Mathematic

• Hilbert functions and set of points in P¹x P¹ , in collaboration with Paola Bonacini, Beiträge zur Algebra und Geometrie , 56 (2015), no.1, 43-61.

• On the Hilbert function of zero-dimensional schemes in P¹x P¹  in collaboration with Paola Bonacini, Collect. Math. 62 (2011), no.1, 57–67

• Separators of fat points in Pⁿ, E. Guardo, L. Marino, A. Van Tuyl, Journal of Algebra, 324, (2010), 1492-1512.

• A characterization of ACM 0-dimensional schemes in Q, Le Matematiche Vol. 64 (2009), no. 2, 41–56.


• Some results on special binomial ideals, Le Matematiche Vol. 61 (2006), pp. 85—107.

• The minimum degree of a surface that passes through all the points of a 0-dimensional scheme but a point P, Contemporary Mathematics, Volume 376,(2005), pp. 315-331.

• Conductor and separating degrees for sets of points in P^r and in P¹x P¹, Bollettino Unione Matematica Italiana (8) 9- B(2006) pp. 397-421.

• On 0-dimensional schemes with all permissible conductor degrees, Rendiconti del circolo matematico di Palermo, Serie II, Tomo LII (2003), pp.263-280.

• Conductor Degree and Socle Degree, in collaboration with Silvia Abrescia and Laura Bazzotti, Le Matematiche Vol.LVI (2001)- Fasc. I, pp.129-148.

 

 

Books

 

P. Bonacini, M.G. Cinquegrani, L. Marino, Algebra Lineare: Esercizi svolti, Ed. Cavallotto,

Catania 2012.

 

 

P. Bonacini, M.G. Cinquegrani, L. Marino, Geometria Analitica: Esercizi svolti, Ed. Cavallotto,

Catania 2012.

 

Talks and posters

Presentation: “On blocking sets in Steiner systems and G-designs”, Istanbul, 4^th Istanbul Design Theory Workshop, September 3- 4, 2018.

 

Presentation: “Perfect Blocking Sets in $P_{3}$-designs”, Combinatorics 2018, Arco (Trento) June 3- June 9, 2018.

 

Presentation: “Nonagon Quadruple Systems: existence, balance, embeddings”, Combinatorics 2016, Maratea (Potenza) May 29- June 4, 2016.

 

Presentation of Poster n.1 with Paola Bonacini entitled “Minimal free resolutions of 0-dimensional schemes in P1XP1” at “GAEL XX1”, held at Stockholm University June 24-28, 2013.


 

Presentation of Poster n.2 with Paola Bonacini entitled “Hilbert functions of 0-dimensional

schemes in P1XP1” at “GAEL XX1”, held at Stockholm University June 24-28, 2013.




Presentation “Zero-dimensional schemes with some properties in common with ACM scheme in

P1xP1”, at the “Seminario congiunto Catania- Messina – Palermo (CA.ME.PA.) ” of Commutative

Algebra and Algebraic Geometry, held in University of Messina, December 1, 2011.


 

Presentation of a joint poster with Paola Bonacini entitled “0-dimensional schemes in P1xP1:

Hilbert functions and minimal free resolutions” at “A Celebration of Algebraic Geometry”, a

conference in honor of Joe Harris’ 60th birthday, held at Harvard University, Boston (USA) August

25-28, 2011.


 

"On 0-dimensional schemes with all permissible conductor degrees” - Conference on Commutative

Algebra with applications in Geometry and Combinatorics. – Piraino (Messina) September 2003

 

"Conductor degrees in P^r"- XV Coloquio Latinoamericano di Algebra- July 2003 Cocoyoc

Mexico

 

 

 

Conferences, meetings, and schools of research attended

 

Geometrical and Combinatorial Aspects of Commutative Algebra, September 16-19, 2009, Villafranca Tirrena, Messina

 

Geometry of projective varieties,

University of Roma La Sapienza, September 2008

 

Commutative Algebra and Algebraic Geometry,

Meeting, University of Catania. 2007

 

Meeting, Commutative Algebra, and Algebraic Geometry, Math Depart of University of Berkeley, California, USA, March 2005.

 

Seminars on Commutative Algebra and Algebraic Geometry

at the Math Depart of Arizona State University, Tempee, Arizona USA, 2004

 

Conferences on Commutative Algebra with applications in Geometry and combinatorics

Piraino(Messina) September 22-25, 2003

 

XV Coloquio Latinoamericano di Algebra. Cocoyoc-Mexico July 20-26, 2003

 

Workshop of algebraic geometry, Politecnico di Torino, September 2002

Conference on zero-dimensional schemes and related topics (in honor of Tony Geramita on the

the occasion on his 60^th birthday) La Perla Ionica (Acireale) Catania June 6-8, 2002

 

Workshop on “Application of Commutative Algebra”, Catania April 3-6, 2002

Conference on Commutative Algebra and Algebraic Geometry (in honor of the 60^th birthday of Silvio Greco) Catania April 11-13, 2001

 

Workshop of algebraic geometry, Politecnico di Torino, September 2002

 

Grostat IV- Workshop on Grobner bases and statistics, Menton September 5-5, 2000, France

 

Pragmatic 2000. Summer school, Catania June 7-23, 2000

 

Giornate di geometria algebrica, Gargnano, May 2000

Workshop on Zero-dimensional schemes and application, Napoli, February 9-12, 2000

Summer school on Computational Algebra “Initial Ideals”, Nordfjorded, August 10-15, 1999

Conference in honor of David Buchsbaum, Catania April 27- May 5, 1998

 

VIEW THE PUBLICATIONS

My predominant area of research is Combinatorics with primary emphasis on Combinatorial Design Theory and Graph Theory.

 

Another rearch field is algebraic geometry. In particular zero-dimensional schemes in P1 × P1, Hilbert functions and minimal free resolutions.