##### Curriculum vitae and Publications

My current research fields are graph theory and designs theory. My research is focusing on existence and balancing problems for G-designs and on blocking sets.

Another research field is algebraic geometry. In this area my results focus on plane sections of curves in P3, on the lifting problem of codimension 2 varieties in a projective space in any characteristic and on zero-dimensional schemes in P1 × P1, in particular studying their Hilbert functions and their minimal free resolutions.

Another research field is algebraic geometry. In this area my results focus on plane sections of curves in P3, on the lifting problem of codimension 2 varieties in a projective space in any characteristic and on zero-dimensional schemes in P1 × P1, in particular studying their Hilbert functions and their minimal free resolutions.

##### Current position

From June 2018 fixed-term reasercher in Geometry at the Mathematic and Computer Science Department of the University of Catania.

##### Abilitation

National Academic Qualification as Associate Professor in Algebra and Geometria, 01/A2 (sector MAT/03-Geometry), from July 31st, 2017 to July 31st, 2023.

##### Past positions

February 2013/January 2018: fixed-term researcher in Geometry at the Mathematic and Computer Science Department of the University of Catania.

May 2008/April 2012: postdoctoral research fellow at the University of Catania in Geometry with the reseach project “Lifting problems of codimension 2 varieties in positive characteristic”.

April 2007/Genuary 2008: research contract at the Department of Mathematics and Computer Science of the University of Catania.

May 2008/April 2012: postdoctoral research fellow at the University of Catania in Geometry with the reseach project “Lifting problems of codimension 2 varieties in positive characteristic”.

April 2007/Genuary 2008: research contract at the Department of Mathematics and Computer Science of the University of Catania.

##### Education

February 2007: Ph.D. in Mathematics at the University of Catania.

Thesis title: “Zero-dimensional schemes and plane sections of space curves”

Advisor: Prof. Rosario Strano.

December 2001: Degree in Mathematics (cum laude) at the University of Catania.

Thesis title: “Hypersurfaces and hyperplane sections”.

Advisor: Prof. Rosario Strano.

Thesis title: “Zero-dimensional schemes and plane sections of space curves”

Advisor: Prof. Rosario Strano.

December 2001: Degree in Mathematics (cum laude) at the University of Catania.

Thesis title: “Hypersurfaces and hyperplane sections”.

Advisor: Prof. Rosario Strano.

##### Publications

- “Blocking sets for C4-designs”, in collaboration with Lucia Marino, preprint.
- “Perfect blocking sets in P3-designs”, in collaboration with Mario Gionfriddo and Lucia Marino, to appear in The Art of Discrete and Applied Mathematics.
- “The spectrum of balanced P^3(1,5)-designs”, in collaboration with Maria Di Giovanni, Mario Gionfriddo, Lucia Marino and Antoinette Tripodi, Contributions to Discrete Mathematics, 12 (1), 2017, 133-142. http://cdm.ucalgary.ca/cdm/index.php/cdm/article/view/549/249
- “On the spectrum of Octagon Quadrangle Systems of any index”, in collaboration with Lucia Marino, Contributions to Discrete Mathematics, 12 (1), 2017, 74-82. http://cdm.ucalgary.ca/cdm/index.php/cdm/article/view/529/243
- “Equitable block colorings for 8-cycle systems”, in collaboration with Lucia Marino, The Australasian Journal of Combinatorics, 69 (2017), no. 2, 184–196. https://ajc.maths.uq.edu.au/pdf/69/ajc_v69_p184.pdf
- “Block colourings of 6-cycle systems”, in collaboration with Mario Gionfriddo and Lucia Marino, Opuscula Math. 37, no. 5 (2017), 647-664. http://www.opuscula.agh.edu.pl/vol37/5/art/opuscula_math_3735.pdf
- “Equitable block colourings for systems of 4-kites”, in collaboration with Mario Gionfriddo and Lucia Marino, Applied Mathematical Sciences, Vol. 11, 2017, no. 21, 1029-1047, https://doi.org/10.12988/ams.2017.69241. http://www.m-hikari.com/ams/ams-2017/ams-21-24-2017/p/bonaciniAMS21-24-2017.pdf
- "Nonagon quadruple systems: existence, balance, embeddings", in collaboration with Mario Gionfriddo and Lucia Marino, The Australasian Journal of Combinatorics, 66 (2016), no. 3, 393-406. http://ajc.maths.uq.edu.au/pdf/66/ajc_v66_p393.pdf
- “Homogeneous edge-coloring of graphs”, in collaboration with Maria Grazia Cinquegrani and Lucia Marino, Utilitas Mathematica, 100 (2016), 269-276. http://arxiv.org/pdf/1203.4531v1.pdf
- “On a 3-uniform path-hypergraph on 5 vertices”, Applied Mathematical Sciences, Vol. 10, 2016, no. 30, 1489-1500. http://dx.doi.org/10.12988/ams.2016.512742 http://www.m-hikari.com/ams/ams-2016/ams-29-32-2016/p/bonaciniAMS29-32-2016.pdf
- “Nestings House-designs”, in collaboration with Mario Gionfriddo and Lucia Marino, Discrete Mathematics, 339 (2016), no. 4, 1291-1299. http://www.sciencedirect.com/science/article/pii/S0012365X15004239
- “Construction of non-cyclic balanced P(3)(1,5)-designs”, in collaboration with Mario Gionfriddo and Lucia Marino, Applied Mathematical Sciences, 9 (2015), no. 126, 6273-6282. http://www.m-hikari.com/ams/ams-2015/ams-125-128-2015/p/gionfriddoAMS125-128-2015-1.pdf
- “Balanced House-systems and Nestings”, in collaboration with Mario Gionfriddo and Lucia Marino, Ars Combinatoria, 121 (2015), 429-436.
- “Equitable tricolourings for 4-cycle systems”, in collaboration with Lucia Marino, Applied Mathematical Sciences, 9 (2015), no. 58, 2881-2887. http://www.m-hikari.com/ams/ams-2015/ams-57-60-2015/p/bonaciniAMS57-60-2015.pdf
- “Hilbert functions and set of points in P1 × P1”, in collaboration with Lucia Marino, Beiträge zur Algebra und Geometrie, 56 (2015), no. 1, 43-61. http://arxiv.org/pdf/1009.4059v2
- “Equitable block colourings”, in collaboration with Lucia Marino, Ars Combinatoria, 120 (2015), 255-258. http://arxiv.org/abs/1406.5454
- “Minimal free resolutions of 0-dimensional schemes in P1 × P1”, in collaboration with Lucia Marino, Algebra Colloquium, 22 (2015), no.1, 97-108, http://arxiv.org/pdf/1108.4007v1
- On the lifting problem in P4 in characteristic p”, Int. Electron. J. Geom., 5 (2012), no. 1, 128-139 , http://www.iejgeo.com/matder/dosyalar/makale-102/bonacini-5-1-2012.pdf
- “On the Hilbert function of zero-dimensional schemes in P1 × P1”, in collaboration with Lucia Marino, Collect. Math. 62 (2011), no.1, 57–67, http://link.springer.com/article/10.1007%2Fs13348-010-0004-x?LI=true
- “Laudal’s Lemma in positive characteristic”, Journal of Algebraic Geometry, 18 (2009), 459–476, http://www.ams.org/journals/jag/2009-18-03/S1056-3911-08-00501-8/
- “Hilbert function of decreasing type in positive characteristic”, Rendiconti del Seminario Matematico dell’Università e del Politecnico di Torino, 67 (2009), no. 1, 41–53, http://seminariomatematico.dm.unito.it/rendiconti/67-1/41.pdf
- “On the plane section of an integral curve in positive characteristic”, Proceedings of the American Mathematical Society, 136 (2008), no. 1, 2289–2297, http://www.ams.org/journals/proc/2008-136-07/S0002-9939-08-09271-X/
- “On a theorem of Faltings on formal functions”, in collaboration with Alessio Del Padrone and Michele Nesci, Le Matematiche, 62 (2007), no. 1, 95–104, http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/17/16
- “Plane sections of space curves in positive characteristic”, Le Matematiche, 61 (2006), no. 1, 3–11, http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/97/81

##### Workshop proceedings

“On the lifting problem in positive characteristic”, Rendiconti dell’Istituto di Matematica dell’Università di Trieste, 47 (2015), 187-202, processing of the workshop “Vector bundles days II” held in Trieste on the occasion of Emilia Mezzetti’s 60th birthday, January 2014. http://rendiconti.dmi.units.it/volumi/47/010.pdf

##### Talks, seminars and posters

- “Equitable block colourings for systems of 4-kites” at the Conference “HyGraDe 2017” held in Sant’Alessio on the occasion of Mario Gionfriddo 70th birthday, June 2017.
- “Equitable block colourings of cycle systems” at the conference “Combinatorics 2016” organized by the University of Basilicata and held in Maratea, May-June 2016.
- “On the lifting problem in P4 in characteristic p” at the workshop “Vector bundles says II” held in Trieste on the occasion of Emilia Mezzetti’s 60th birthday, January 2014.
- Presentation of two joint poster with Lucia Marino entitled “Hilbert functions of 0-dimensional schemes in P1xP1” and “Minimal free resolutions of 0-dimensional schemes in P1xP1” at the conference “Geométrié Algébrique en Liberté - GAeL XXI” held in Stockholm at Stockholm University, June 2013.
- “0-dimensional schemes in P1xP1” at the workshop “Syzygies in Berlin”, held in Berlin, May 2013.
- Presentation of a joint poster with Lucia Marino 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, August 2011.
- “Zero-dimensional schemes in P1xP1”, at the “Seminario congiunto Catania - Messina - Palermo” of Commutative Algebra and Algebraic Geometry, held in Catania, May 2011.
- “Laudal’s Lemma in positive characteristic”, at the “Workshop on commutative algebra, algebraic geometry and applications to different fields”, held in Brolo (Messina), September 2007.
- “Plane sections of space curves in characteristic p”, at the “School on characteristic p methods in Algebraic Geometry”, held in Drobeta Turnu Severin (Romania), July 2007.
- “Plane sections of integral space curves”, at the conference “Giornate di Geometria Algebrica ed Argomenti Correlati VIII”, held at SISSA (Trieste), May 2006 (on invitation).

##### Schools and workshops attended

- “Seminario congiunto Catania - Messina - Palermo di Algebra Commutativa e Geometria Algebrica'”, held in Palermo at the Palermo University, 27/02/2012.
- “Classical and recent aspects in the study of projective varieties”, held in Genova, at the Genova University, 21/01-22/01/2010.
- Workshop “Geometrical and combinatorial aspects of Commutative Algebra”, held in Villafranca Tirrena (Messina), 16/09-19/09/2009.
- “Workshop on Algebraic Surfaces”, held at the Centro di Ricerca Matematica Ennio De Giorgi (Pisa), 29-31/10/2008.
- Workshop on “Geometry of Projective Varieties”, Rome, Sapienza University of Rome, 30/09 - 04/10/2008.
- “Workshop on commutative algebra, algebraic geometry and applications to different fields”, Brolo (Messina - Italy), 12-15/09/2007.
- “School on characteristic p methods in Algebraic Geometry”, Drobeta Turnu-Severin (Romania), 13-19/07/2007.
- “NATO Advanced Study Institute on Higher-dimensional Geometry over Finite Fields”, Gottingen (Germany), Georg-August-Universitat of Gottingen, 25/06-06/07/2008.
- “School of Algebraic Geometry “P.R.A.G.MAT.I.C.”, held in Catania at the University of Catania, 04-23/09/2006.
- “Giornate di Geometria Algebrica ed Argomenti Correlati VIII”, held in Trieste at SISSA, 26-29/05/2006.
- “Winter School on Commutative Algebra and applications” held in Barcelona (Spain) at the University of Barcelona, 30/01-3/02/2006.
- “Summer Research Institute in Algebraic Geometry”, held in Seattle (USA) at the University of Washington, 30/07-6/08/2005.
- “Giornata di studio su Algebra Commutativa e Geometria Algebrica in onore del Prof. Rosario Strano per il suo 60° compleanno”, held in Piraino (ME), 01/02/2005.
- “Workshop on Commutative Algebra and Algebraic Geometry”, held in Piraino (ME), 20/09-23/09/2004.
- “School on Commutative Algebra and interactions with Algebraic Geometry and Combinatorics”, held in Trieste atThe Abdus Salam International Center for Theoretical Physics, 24/05-11/06/2004.
- “School and Workshop on Polynomial Interpolation and Projective Embedding”, held in Torino at the Politecnico di Torino, 15/09-20/09/2003.
- Summer School “Scuola Matematica Interuniversitaria” in Perugia. Courses: Algebra and Algebraic Geometry, 28/07-31/08/2002.

##### Other activities

Reviewer for Mathscinet and Zentralblatt MATH.

##### Didactic activity

- Exercises for the course of “Combinatorial Geometry” for students of the Master’s Degree in Mathematics at the University of Catania, 2015/16.
- Exercises for the course of “Linear Algebra and Geometry” for students of the Bachelor’s Degree in Computer Engineering, Electronic Engineering and Industrial Engineering at the University of Catania, 2014/15.
- Course of “Linear Algebra and Geometry” for students of the Bachelor’s Degree in Computer Engineering and Electronic Engineering at the University of Catania, 2014/15.
- Exercises for the course of “Discrete models” for students of the Bachelor’s Degree in Mathematics at the University of Catania, 2014/15.
- Course of “Linear Algebra and Geometry” for students of the Bachelor’s Degree in Computer Engineering and Electronic Engineering at the University of Catania, 2013/14.
- Course of “Linear Algebra and Geometry” for students of the Bachelor’s Degree in Computer Engineering and Electronic Engineering at the University of Catania, 2012/13.
- Exercises for the course of “Linear Algebra and Geometry” for students of the Bachelor’s Degree in Computer Engineering, Electronic Engineering, Civil Engineering and Industrial Engineering at the University of Catania, 2011/12.
- Exercises for the course of “Linear Algebra and Geometry” for students of the Bachelor’s Degree in Computer Engineering, Electronic Engineering and Industrial Engineering at the University of Catania, 2010/11.
- Course of “Linear Algebra and Geometry” for students of Telecommunications Engineering at the University of Catania, 2009/10.
- Exercises for the course of “Linear Algebra and Geometry” for students of the Bachelor’s Degree in Computer Engineering and Architecture and Building Engineering at the University of Catania, 2009/10.
- Course of “Geometry” for students of Environmental and Urban Renewal and Construction Engineering at the University of Catania, 2008/09.
- Exercises for the course of “Linear Algebra and Geometry” for students of the Bachelor’s Degree in Computer Engineering, Telecommunications Engineering and Architecture and Building Engineering at the University of Catania, 2008/09.
- Exercises for the course of “Geometry” for students of the Bachelor’s Degree in Computer Engineering, Telecommunications Engineering, Architecture and Building Engineering and Environmental and Urban Renewal and Construction Engineering at the University of Catania, 2007/08.
- Exercises for the course of “Principles of Mathematics” for students of the Bachelor’s Degree in Biological Sciences at the University of Catania, 2006/07.
- Exercises for the course of “Geometry” for students of the Bachelor’s Degree in Civil Engineering and Managerial Engineering at the University of Catania, 2003/04.