Haute Ecole Pédagogique BEJUNE - Suisse
Giuseppe Melfi started his studies in mathematics at the Scuola Normale Superiore of Pisa in 1987. In 1994 he started the at the university of Pisa a doctoral thesis. He was interested in some convolution formulas published by Srinivasa Ramanujan in 1916, and remained without proof for almost eighty years. Using the theory of modular forms, he provided a proof of all Ramanujan's formulas, and proposed some new ones that Ramanujan had not found. These results were announced at an international congress in Eger, Hungary, in the summer of 1996. On this occasion he met Paul Erdös. Their collaboration then resulted in an paper that appeared in 1999 on sum-free sequences. In '90s he has worked in particular with Don Zagier, Umberto Zannier and Jean-Marc Deshouillers. In 2000 he was appointed at the University of Neuchâtel, where at present he is professor.