Giuseppe Melfi is an Italo

Italy

Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

-Swiss

Switzerland

Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....

mathematician. He got his PhD in mathematics in 1997 at the University of Pisa

University of Pisa

The University of Pisa , located in Pisa, Tuscany, is one of the oldest universities in Italy. It was formally founded on September 3, 1343 by an edict of Pope Clement VI, although there had been lectures on law in Pisa since the 11th century...

. After some years spent at the University of Lausanne

University of Lausanne

The University of Lausanne in Lausanne, Switzerland was founded in 1537 as a school of theology, before being made a university in 1890. Today about 12,000 students and 2200 researchers study and work at the university...

, he works now at the University of Neuchâtel

University of Neuchâtel

The University of Neuchâtel is a French-speaking university in Neuchâtel, Switzerland. The University has five faculties and more than a dozen institutes, including arts and human sciences, natural sciences, law, economics and theology. The Faculty of Arts and Human Sciences is the largest...

, where is a lecturer. His major contributions are in the theory of practical number

Practical number

In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n...

s, where he proved two conjectures; in modular forms he found new Ramanujan-type identities

Eisenstein series

Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written down directly...

 for the sum-of-divisor functions

Divisor function

In mathematics, and specifically in number theory, a divisor function is an arithmetical function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer. It appears in a number of remarkable identities, including relationships...

; other topics of research include sum-free sequences in a joint work with Paul Erdős

Paul Erdos

Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...

 and other problems in elementary number theory

Number theory

Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

.

In applied mathematics his research interests include probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 and simulation

Simulation

Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

.

External links

• Giuseppe Melfi's home page
• The proof of conjectures on practical numbers and the joint work with Paul Erdos on Zentralblatt
  Zentralblatt MATH
  Zentralblatt MATH is a service providing reviews and abstracts for articles in pure and applied mathematics, published by Springer Science+Business Media. It is a major international reviewing service which covers the entire field of mathematics...
  
  .
• Tables of practical numbers compiled by Giuseppe Melfi