Martino Garonzi

"Le ombre lunghe dei sacerdoti costrinsero il sogno in un cerchio di voci." (F. De André, "Il sogno di Maria")

I'm a PHD student of mathematics in Padova (Italy). The address of the math department (where I work) is Via Trieste 63, 35121, Padova (Italy). The telephone number of my office is 049 827 1260/1261.

My supervisor is Andrea Lucchini. My interests are in algebra, and especially in group theory. I work on the following subject: given a finite group G, define the "sigma" of this group to be the least number of proper subgroups of G needed to cover G set-theoretically. The problem is to investigate the properties of this sigma. Here are my four publications, in chronological order:

• Finite Groups that are union of at most 25 proper subgroups. Journal of Algebra and its Applications, ISSN: 02194988. It is about the results in my master thesis, which you can find here (in Italian).
• (with Attila Maroti) Covering certain wreath products with proper subgroups. J. Group Theory 14 (2011), no. 1, 103–125,
• (with Andrea Lucchini) Direct Products of Finite Groups as Union of Proper Subgroups, Arch. Math. (Basel) 95 (2010), no. 3, 201-206.
• Covering Monolithic Groups with Proper Subgroups. Communications in algebra, ID: LAGB-2011-2732.R1.

At the end of the first three years of university I did a short work about the simplicity of the projective special linear group and the symplectic group (nothing new).

I am writing a pdf file about all the algebra that I learned in my life (obviously I'm far from being finished), you can find it here. Be aware of the mistakes (I find mistakes anytime I look at it). Ah, unfortunately it is in Italian. I will try to produce an english version of it.

My e-mail address is mgaronzi@math.unipd.it.

• I am a chess player. I have written something about chess, for example this, this and this (all in Italian, sorry). As you can notice, I like chess puzzles and endgames. This is my Fide Chess Profile.
• I am vegan. Why? There are several reasons. The main reason is this. In order to know more about this interesting subject see here (English!).
• I like to speak French. I was in France 10 months (in the university Paris 11 in Orsay) with the Erasmus (Algant) program, and sometimes I miss it.
• I am a moderator in this Italian forum of mathematics (www.matematicamente.it).
• I like the german language. I have written something (very short and simple) in german, for example this and this.
• I like Fabrizio De André's music. Very much. He was a genius. Here are the sentences of him that I like most:
  • "Le ombre lunghe dei sacerdoti costrinsero il sogno in un cerchio di voci" (Il Sogno di Maria).
  • "Uomini, poiché all'ultimo minuto non vi assalga il rimorso ormai tardivo per non aver pietà giammai avuto e non diventi rantolo il respiro, sappiate che la morte vi sorveglia gioir nei prati o fra i muri di calce, come crescere il gran guarda il villano finché non sia maturo per la falce." (Corale, Leggenda Del Re Infelice).
  • "E adesso che ho bruciato venti figli sul mio letto di sposo, che ho scaricato la mia rabbia in un teatro di posa, che ho imparato a pescare con le bombe a mano, che mi hanno scolpito in lacrime sull'arco di Traiano, con un cucchiaio di vetro scavo nella mia storia. Ma colpisco un po' a casaccio perché non ho più memoria. E a un dio senza fiato non credere mai." (Coda di Lupo).
  • "Stelle già dal tramonto si contendono il cielo a frotte, luci meticolose nell'insegnarti la notte. Un asino dai passi uguali, compagno del tuo ritorno, scandisce la distanza lungo il morire del giorno." (Il Ritorno Di Giuseppe).
  • ""E se gli sparo in fronte o nel cuore soltanto il tempo avrà per morire, ma il tempo a me resterà per vedere, vedere gli occhi di un uomo che muore". E mentre gli usi questa premura quello si volta , ti vede, ha paura, ed imbracciata l'artiglieria non ti ricambia la cortesia." (La Guerra di Piero).
  • "Tu prova ad avere un mondo nel cuore, e non riesci ad esprimerlo con le parole. E la luce del giorno si divide la piazza tra un villaggio che ride e te, lo scemo che passa. E neppure la notte ti lascia da solo: gli altri sognan se stessi e tu sogni di loro." (Un Matto).
  • "Ama e ridi se amor risponde, piangi forte se non ti sente. Dai diamanti non nasce niente, dal letame nascono i fior." (Via del Campo).
  • "Il cuore impazzì e ora no, non ricordo, da quale orizzonte sfumasse la luce." (Un Malato di Cuore).
  • "Vuoi davvero lasciare ai tuoi occhi solo i sogni che non fanno svegliare?" (La Canzone del Padre).
  • "Se un mattino fra i capelli troverai un po' di neve, nel giardino del tuo amore verrò a raccogliere il bucaneve." (La Stagione del Tuo Amore).
  • "Passa il tempo sopra il tempo, ma non devi aver paura. Sembra correre come il vento, però il tempo non ha premura." (La Stagione del Tuo Amore).
• I don't believe to any kind of god. I am an atheist. (Repetita Iuvant.) I need to talk about this property of mine because sometimes people (in Italy) think that if one doesn't express any religious attitude, he/she is catholic. This is somehow curious: why don't they automatically think that his/her unique god is a pumpkin? Or maybe a pomegranate?
• I like cats. I think that if there is some universal truth giving a sense to life, it has something to do with cats.
• I like to read, but I often don't manage to finish a book unless I like it very much. My favourite book is One Hundred Years Of Solitude (G. G. Marquez). Here is a fantastic extract:
  • El martes a las cinco de la mañana José Arcadio habia tomado el café y soltado los perros, cuando Rebeca cerró la ventana se agarró de la cabecera de la cama para no caer. «Ahí lo trae -suspiró-. Qué hermoso está». José Arcadio se asomó a la ventana, y lo vio, trémulo en la claridad del alba, con unos pantalones que habían sido suyos en la juventud. Estaba ya de espaldas al muro y tenía las manos apoyadas en la cintura porque los nudos ardientes de las axilas le impedían bajar los brazos. «Tanto joderse uno - urmuraba el coronel Aureliano Buendía-. Tanto joderse para que lo maten a uno seis maricas sin poder hacer nada,» Lo repetía con tanta rabia, que casi parece fervor, y el capitán Roque Carnicero se conmovió porque creyó que estaba rezando. Cuando el pelotón lo apuntó, la rabia se había materializado en una sustancia viscosa y amarga que le adormeció la lengua y lo obligó a cerrar los ojos. Entonces desapareció el resplandor de aluminio del amanecer, y volvió verse a sí mismo, muy niño, con pantalones cortos y un lazo en el cuello, y vio a su padre en una tarde espléndida conduciéndolo al interior de la carpa, y vio el hielo.
• I have a blog.

• 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."