Martino Garonzi

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UNTIL JANUARY 31ST 2015
Postdoctoral fellow in Mathematics in Padova (Italy).
Mathematics Department (Torre Archimede)
Via Trieste 63, 35121, Padova (Italy).
Office 334, Floor 3.
Phone number: 0039 049 827 1328.
E-mail address: mgaronzi@math.unipd.it.

Starting from February 1st 2015 I will be a Postdoc in the University of Brasilia.

My interests are in algebra, and especially in group theory. This is my Ph.D Thesis.

Here are my publications:

• Finite Groups that are union of at most 25 proper subgroups, J. Algebra Appl. 12 (2013), no. 4, 1350002, 11 pp. It is about the results in my master thesis, which you can find here (in Italian).
• Covering certain wreath products with proper subgroups, J. Group Theory 14 (2011), no. 1, 103–125 (joint work with Attila Maróti).
• Direct Products of Finite Groups as Union of Proper Subgroups, Arch. Math. (Basel) 95 (2010), no. 3, 201-206 (joint work with Andrea Lucchini).
• Covering certain Monolithic Groups with Proper Subgroups, Comm. Algebra 41 (2013), no. 2, 471–491.
• Covering Monolithic Groups with Proper Subgroups, Int. J. Group Theory 2 (2013), no. 1, 131–144. (for the Prooceedings of the conference "Ischia Group Theory 2012").
• Covers and Normal Covers of Finite Groups, J. Algebra 422 (2015), 148–165 (joint work with Andrea Lucchini).
• Factorizing a Finite Group into Conjugates of a Subgroup, J. Algebra 418 (2014), 129–141. (joint work with Dan Levy).
• On the number of conjugacy classes of a permutation group (joint work with Attila Maróti). Submitted to Journal of Combinatorial Theory, Series A, and accepted.
• Inequalities detecting structural properties of a finite group (joint work with Massimiliano Patassini). Submitted.
• Irredundant and minimal covers of finite groups (joint work with Andrea Lucchini). Submitted to Communications in Algebra, and accepted.
• Groups equal to a product of three conjugate subgroups (joint work with John Cannon, Dan Levy, Attila Maróti, Iulian I. Simion). Submitted to Israel Journal of Mathematics, and accepted.
• Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent (joint work with Dan Levy, Attila Maróti, Iulian I. Simion). Submitted.

• Here are the Slides of my PhD defence I had in the University of Padova on March 1st 2013.
• Here are some Slides about the covering number of a direct product of groups. They were meant to be the slides of a talk but I ended up giving it at the blackboard.
• Here are the Slides of the talk I gave at the university of Birmingham (UK) on November 9th 2012.
• Here are the Slides of the talk I gave in Padova (Italy) on February 27th 2013 (Seminario Dottorato). It is supposed to be a basic and understandable introduction to the topic of my Ph.D thesis. Here is a detailed note.
• Here are the Slides of the talk I gave at the Groups St Andrews 2013 Conference in St Andrews (Scotland) on August 5th 2013.
• Here are the Slides of the talk I gave at the Ischia Group Theory 2014 Conference in Ischia (Naples, Italy) on April 4th 2014.
• Here are the Slides of the talk I gave in Padova (Italy) on April 30th 2014 (Seminario Dottorato). It is supposed to be a basic and understandable introduction to representation theory of groups. Here is a detailed note.
• Here are the Slides of the talk I gave in Padova (Italy) on December 3rd 2014 and in Brasilia (Brasil) on February 10th 2015. Both at the blackboard.
• Here are the Slides of the talk I gave in Brasilia (Brasil) on March 13th 2015. At the blackboard. English version.

• Pagina del prof. Andrea Lucchini, titolare del corso.
• Pagina del prof. Federico Menegazzo, titolare del corso di Algebra 2 dell'a.a. 2012-2013.
• Esercizi su gruppi e polinomi.
• Registro cose fatte.
• Alcuni esercizi svolti.
• Compitino del 17/11/2014: Tema A, Tema B. Svolgimento del Tema A.
• Compitino del 19/01/2015: Testo, Risoluzione.
• Testo dell'appello del 4 febbraio 2015.
• Approfondimenti: a.a 2013-2014, a.a 2014-2015. A puro scopo di curiosità, e si tratta di cose ben note.

TESTI DI ESAMI. Compitino del 12/11/2013: Tema A, Tema B, Risoluzione. Compitino del 21/01/2014: Testo, Risoluzione. Appello del 05/02/2014: Testo, Risoluzione. Appello del 25/02/2014: Testo, Risoluzione. Appello del 16/06/2014: Testo, Risoluzione. Appello del 16/07/2014: Testo, Risoluzione. Appello del 15/09/2014: Testo, Risoluzione. Soluzione del primo compitino 22/11/2012 (tema B), Soluzione del secondo compitino 31/01/2013 (tema A), Soluzione del primo appello 04/02/2013 (tema B), Testo del secondo appello 08/07/2013, Testo dell'appello del 06/07/2012. Segnalo anche la pagina di Gabriele Fusacchia, dove trovate altro materiale, tra cui esami passati.

• I am a chess player. This is my Fide Chess Profile.
• I am quite a strict vegetarian. More precisely I am vegetarian and I preferably don't eat anything containing animal products, namely, dairy products. Why? There are several reasons. The main reason is this.
• I like languages, particularly English French and German. I have written something (very short and simple) in German, for example this and this.
• I was a moderator in this Italian forum of mathematics (www.matematicamente.it/forum).
• I have a blog.
• I like origami.
• I am doing Tennis, Yoga and Acting classes.

• The following is a great extract from the book of Robert Pirsig "Zen and the Art of Motorcycle Maintenance":
  
  "He'd been innovating extensively. He’d been having trouble with students who had nothing to say. At first he thought it was laziness but later it became apparent that it wasn’t. They just couldn’t think of anything to say. One of them, a girl with strong-lensed glasses, wanted to write a five-hundred-word essay about the United States. He was used to the sinking feeling that comes from statements like this, and suggested without disparagement that she narrow it down to just Bozeman.
  
  When the paper came due she didn’t have it and was quite upset. She had tried and tried but she just couldn’t think of anything to say. He had already discussed her with her previous instructors and they’d confirmed his impressions of her. She was very serious, disciplined and hardworking, but extremely dull. Not a spark of creativity in her anywhere. Her eyes, behind the thick-lensed glasses, were the eyes of a drudge. She wasn’t bluffing him, she really couldn’t think of anything to say, and was upset by her inability to do as she was told. It just stumped him. Now he couldn’t think of anything to say. A silence occurred, and then a peculiar answer: "Narrow it down to the main street of Bozeman." It was a stroke of insight.
  
  She nodded dutifully and went out. But just before her next class she came back in real distress, tears this time, distress that had obviously been there for a long time. She still couldn’t think of anything to say, and couldn’t understand why, if she couldn’t think of anything about all of Bozeman, she should be able to think of something about just one street. He was furious. "You’re not looking!" he said. A memory came back of his own dismissal from the University for having too much to say. For every fact there is an infinity of hypotheses. The more you look the more you see. She really wasn’t looking and yet somehow didn’t understand this. He told her angrily, "Narrow it down to the front of one building on the main street of Bozeman. The Opera House. Start with the upper left-hand brick."
  
  Her eyes, behind the thick-lensed glasses, opened wide. She came in the next class with a puzzled look and handed him a fivethousand-word essay on the front of the Opera House on the main street of Bozeman, Montana. "I sat in the hamburger stand across the street," she said, "and started writing about the first brick, and the second brick, and then by the third brick it all started to come and I couldn’t stop. They thought I was crazy, and they kept kidding me, but here it all is. I don’t understand it."
  
  Neither did he, but on long walks through the streets of town he thought about it and concluded she was evidently stopped with the same kind of blockage that had paralyzed him on his first day of teaching. She was blocked because she was trying to repeat, in her writing, things she had already heard, just as on the first day he had tried to repeat things he had already decided to say. She couldn’t think of anything to write about Bozeman because she couldn’t recall anything she had heard worth repeating. She was strangely unaware that she could look and see freshly for herself, as she wrote, without primary regard for what had been said before. The narrowing down to one brick destroyed the blockage because it was so obvious she had to do some original and direct seeing."